Free Printable Composition and Inverse Functions

1.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

2.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(-1\right)\right)$

a)

2

b)

15

c)

7

d)

-9

3.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

4.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

5.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(f\circ g\right)\left(2\right)$

a)

$\frac{1}{4}$

b)

$\frac{1}{8}$

c)

$\frac{7}{2}$

d)

8

6.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ g\right)\left(-4\right)$

a)

44

b)

-40

c)

-30

d)

-28

7.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ f\right)\left(x\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

8.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $f\left(g\left(x\right)\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

9.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\sqrt{x}$ find $g\left(f\left(x\right)\right)$

a)

$x^4$

b)

$x$

c)

$\sqrt[]{x}$

d)

$x^2$

10.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\frac{1}{x^2}$ find $\left(f\circ g\right)\left(-1\right)$

a)

$\frac{1}{4}$

b)

$1$

c)

$-1$

d)

$-\frac{1}{4}$

11.

When $f(x)=x^2+9$ and $g(x)=x-9$ , find $f(x)-g(x)$

a)

$x^2+x+9$

b)

$x^2-x+9$

c)

$x^2-x$

d)

$x^2-x+18$

12.

When $f(x)=9-3x$ and $g(x)=5x-7$ , find $f(x)+g(x)$

a)

$14x-10$

b)

$-8x+2$

c)

$2x+2$

d)

$2x-2$

13.

If $g\left(x\right)=x^2+6$ and $f\left(x\right)=2x-4$ , find $f\left(g\left(x\right)\right)$

a)

$2x^2-12x-4$

b)

$2x^2+12x-4$

c)

$2x^2+8$

d)

$x^3-2x^2+1$

14.

a)

7

b)

6

c)

11

d)

None of the Above

15.

$g\left(f\left(2\right)\right)$

a)

5

b)

3

c)

-1

d)

2

16.

If $f\left(x\right)=2x+3$ and $g\left(x\right)=-3x-4$ , find $f\left(x\right)\cdot g\left(x\right)$

a)

$-6x^2-17x-12$

b)

$6x^2+x-12$

c)

$-x-1$

d)

$5x+7$

17.

Find f(2).

a)

-2

b)

-18

c)

24

d)

6

18.

Find g(5)

a)

3375

b)

375

c)

25

d)

45

19.

f(x-2)

a)

2x² - 13x + 18

b)

2x² - 5x + 18

c)

2x² - 8x + 3

d)

2x² - 13x + 2

20.

g(4x)

a)

1728x³

b)

12x³

c)

192x³

d)

36x³

21.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

22.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

23.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

24.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

a)

182

b)

40

c)

61

d)

None of the Above

25.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

a)

16

b)

4

c)

-4

d)

None of these.

26.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

27.

g(a) = 4a + 1

h(a) = -3a + 2

Find g(h(1))

a)

3

b)

-3

c)

21

d)

-21

28.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(x))

a)

3x + 8

b)

3x - 2

c)

3x + 4

d)

None of these.

29.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

30.

If f(x) = x-1 and g(x) = 2x,

what is and g(f(x)) ?

a)

2x²-1

b)

2x-1

c)

2x-2

d)

x-2

31.

f(n)=2n+1
g(n)=3n
Find f(n)+g(n)

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

32.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

33.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(-1\right)\right)$

a)

2

b)

15

c)

7

d)

-9

34.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

35.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

36.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(f\circ g\right)\left(2\right)$

a)

$\frac{1}{4}$

b)

$\frac{1}{8}$

c)

$\frac{7}{2}$

d)

8

37.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ g\right)\left(-4\right)$

a)

44

b)

-40

c)

-30

d)

-28

38.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ f\right)\left(x\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

39.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $f\left(g\left(x\right)\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

40.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\sqrt{x}$ find $g\left(f\left(x\right)\right)$

a)

$x^4$

b)

$x$

c)

$\sqrt[]{x}$

d)

$x^2$

41.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\frac{1}{x^2}$ find $\left(f\circ g\right)\left(-1\right)$

a)

$\frac{1}{4}$

b)

$1$

c)

$-1$

d)

$-\frac{1}{4}$

42.

When $f(x)=x^2+9$ and $g(x)=x-9$ , find $f(x)-g(x)$

a)

$x^2+x+9$

b)

$x^2-x+9$

c)

$x^2-x$

d)

$x^2-x+18$

43.

When $f(x)=9-3x$ and $g(x)=5x-7$ , find $f(x)+g(x)$

a)

$14x-10$

b)

$-8x+2$

c)

$2x+2$

d)

$2x-2$

44.

If $g\left(x\right)=x^2+6$ and $f\left(x\right)=2x-4$ , find $g\left(f\left(x\right)\right)$

a)

$2x^2-12x-4$

b)

$2x^2+12x-4$

c)

$4x^2-16x+22$

d)

$x^3-2x^2+1$

45.

Perform the indicated operation.

a)

A

b)

B

c)

C

d)

D

46.

f(n)=x²+1
g(n)=2x-5
Find f(n)-g(n)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

47.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

48.

What is the inverse of the points (1,3)(2,4)(6,2)

a)

(2,6)(3,1)(4,2)

b)

(-3,-1)(-4,-2)(-2,-6)

c)

(1,3)(2,4)(6,2)

d)

(-1,-3)(-2,-4)(-6,-2)

49.

Find the inverse
f(x)=2x-2

a)

f^-1(x)=1/2x+1

b)

f^-1(x)=-2-1/2x

c)

f^-1(x)=-7/3x-20/3

d)

2-2/5x

50.

Find the inverse
f(x)=2x-2

a)

f^-1(x)=1/2x+1

b)

f^-1(x)=-2-1/2x

c)

f^-1(x)=-7/3x-20/3

d)

2-2/5x

51.

Find the inverse
f(x)= x⁴- 2

a)

∜(x+2)

b)

(x+2)⁴

c)

-1+2x⁴

d)

∜2x

52.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

53.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = - 4x - 3

54.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

55.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

56.

When finding the inverse of a relation,
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

a)

solve for y

b)

replace y with f^-1(x)

c)

solve for x

d)

find the greatest common factor

57.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 1/4x + 7/4

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

58.

Find the inverse of f(x) = 5/11x +10

a)

f^-1(x) = 11/5(x - 10)

b)

f^-1(x) = 5/11x - 22

c)

f^-1(x) = 11/5x - 10

d)

None of the above

59.

Find the inverse of f(x) = -2/3x + 1/4

a)

f^-1(x) = -3/2x + 3/8

b)

f^-1(x) = 3/2x - 3/8

c)

f^-1(x) = -3/2x + 8/3

d)

f^-1(x) = 3/2x + 3/8

60.

Given that f(x) = 3x + 5 and g(x) = 1/3x + 5, find f(g(x)). Are the two functions inverses of each other?

a)

x + 20 ; Yes they are inverses

b)

x + 20 ; No, they are not inverses

c)

x ; Yes they are inverses

d)

x ; No, they are not inverses

61.

What is the approximate solution to the equation 3^x-1 = 4^{2x + 5}

a)

3.875

b)

1.262

c)

-2.354

d)

-4.797

62.

a)

A

b)

B

c)

C

d)

D

63.

a)

A

b)

B

c)

C

d)

D

64.

$f\left(x\right)=3x$
Find $f^{-1}\left(x\right)$

a)

$\frac{x}{3}$

b)

$\frac{3}{x}$

c)

$0.3x$

d)

$x\times3$

65.

$f\left(x\right)=7x$
Find $f^{-1}\left(x\right)$

a)

$\frac{x}{7}$

b)

$\frac{7}{x}$

c)

$0.7x$

d)

$x\div\frac{1}{7}$

66.

$g\left(x\right)=\frac{x}{8}$
Find $g^{-1}\left(x\right)$

a)

$\frac{8}{x}$

b)

$8x$

c)

$\frac{1}{8}x$

d)

$x\div8$

67.

$g\left(x\right)=\frac{1}{3}x$
Find $g^{-1}\left(x\right)$

a)

$\frac{3}{x}$

b)

$3x$

c)

$\frac{x}{3}$

d)

$x\div3$

68.

Select the two functions which are inverses of each other:

a)

$x+10$

b)

$x-10$

c)

$\frac{x}{10}$

d)

$\frac{10}{x}$

69.

Select the two functions which are inverses of each other:

a)

$x-4$

b)

$4x$

c)

$\frac{x}{4}$

d)

$\frac{4}{x}$

70.

$f\left(x\right)=5x+1$
Find $f^{-1}\left(x\right)$

a)

$\frac{x-5}{1}$

b)

$\frac{x}{5}-1$

c)

$x-\frac{1}{5}$

d)

$\frac{x-1}{5}$

71.

$f\left(x\right)=\frac{2x}{7}$
Find $f^{-1}\left(x\right)$

a)

$\frac{7x}{2}$

b)

$\frac{2}{7}x$

c)

$7x\times2$

d)

$2x\times7$

72.

$f\left(x\right)=\frac{x-2}{6}$
Find $f^{-1}\left(x\right)$

a)

$\frac{x-6}{2}$

b)

$6x+2$

c)

$2x+6$

d)

$6\left(x+2\right)$

73.

$f\left(x\right)=\frac{8x-3}{5}$
Find $f^{-1}\left(x\right)$

a)

$5\left(8x+3\right)$

b)

$\frac{5x}{8}+3$

c)

$\frac{5\left(x+3\right)}{8}$

d)

$\frac{5x+3}{8}$

74.

$f\left(x\right)=\frac{6x}{5}+3$
Find $f^{-1}\left(x\right)$

a)

$\frac{5x-3}{6}$

b)

$\frac{5\left(x-3\right)}{6}$

c)

$\frac{5x}{6}-3$

d)

$\frac{5x}{6}+3$

75.

$f\left(x\right)=\frac{3x+10}{7}$
Find $f^{-1}\left(x\right)$

a)

$7x-\frac{10}{3}$

b)

$\frac{7x}{3}-10$

c)

$\frac{7\left(x-10\right)}{3}$

d)

$\frac{7x-10}{3}$

76.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

77.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

78.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

79.

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

a)

(1, 2) (3, 8) (-3, 6)

b)

(1, 2) (8, 3) (-3, 6)

c)

(-1, -2) (-3, -8) (3, -6)

d)

(2, 1) (8, 3) (6, -3)

80.

If the equation of f(x) goes through (-1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, -1) and (6, 4)

81.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

82.

If f^-1(-25) = 7 then what is f(7) =

a)

25

b)

7

c)

No enough information.

d)

-25

83.

Which is the inverse of the table?

a)

b)

c)

d)

84.

Are these the graphs of two inverse functions?

a)

Yes

b)

No

c)

No way to tell

85.

When finding the inverse of a relation,
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

a)

solve for y

b)

replace y with f^-1(x)

c)

solve for x

d)

find the greatest common factor

86.

What is the FIRST step I need to take to solve for x in the following equation?

a)

Add 9 to both sides

b)

Take the square root of both sides

c)

Divide both sides by 49

d)

Multiply both sides by 9

87.

Are the following inverses of each other?

a)

True

b)

False

88.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

89.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

90.

Was the inverse function found correctly?

a)

no,

b)

yes

91.

$f\left(x\right)=3x$
Find $f^{-1}\left(x\right)$

a)

$\frac{x}{3}$

b)

$\frac{3}{x}$

c)

$0.3x$

d)

$x\times3$

92.

$f\left(x\right)=5x+1$
Find $f^{-1}\left(x\right)$

a)

$\frac{x-5}{1}$

b)

$\frac{x}{5}-1$

c)

$x-\frac{1}{5}$

d)

$\frac{x-1}{5}$

93.

$f^{-1}\left(x\right)=\frac{1}{3}x+\frac{5}{3}$ , find the original function and type it below using function notation.

(a)

94.

$g\left(x\right)=-7x^5+7$ Find the inverse of the function.

a)

$g^{-1}\left(x\right)=^5\sqrt{\frac{x-7}{7}}$

b)

$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$

c)

$g^{-1}\left(x\right)=^5\sqrt{-\frac{x-7}{7}}$

d)

$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$

95.

Given the inverse of a function. Using function notation, type the original function (Hint: Use the carat (^) symbol for the exponent).
$f^{-1}\left(x\right)=^3\sqrt{4-x}$

(a)

96.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

97.

The inverse has been reflected over which line?

a)

y = x

b)

x = 0

c)

y = 0

d)

x = -y

98.

Which of the following is NOT TRUE about inverse functions?

a)

Inverse functions are reflections of each other over the line y = x.

b)

You find the inverse by switching x and y in the equation.

c)

The domain of a function always becomes the domain of its inverse.

d)

The domain of a function always becomes the range of its inverse.

99.

What are the missing values if g(x)=f^-1(x)?

a)

(9,-5)

b)

(-9,-5)

c)

(5,9)

d)

(-9,5)

100.

What is the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

101.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

102.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

103.

What is the best description?

a)

They are both functions, but not inverse functions.

b)

They are inverse functions.

c)

They are reflected over y=x, but they are not both functions.

d)

They are not reflected over y=x, and they are not both functions.

104.

What is the best description?

a)

They are both functions, but not inverse functions.

b)

They are inverse functions.

c)

They are reflected over y=x, but they are not both functions.

d)

They are not reflected over y=x, and they are not both functions.

105.

Which graph represents f^-1(x) over the same domain?

a)

b)

c)

d)

106.

f(x) = -4x - 12

What is f^-1(x)?

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

107.

Which is f ^-1(x)?

a)

f^-1(x) = 5x + 3

b)

f^-1(x) = 5x - 3

c)

f^-1(x) = 5x - 15

d)

f^-1(x) = 1/5(x) + 3/5

108.

Which is f ^-1(x)?

a)

f^-1(x) = 3x + 5

b)

f^-1(x) = 3x - 5

c)

f^-1(x) = 3x - 15

d)

f^-1(x) = 3x + 15

109.

Which graph represents the functions f(x) and f^-1(x)?

a)

b)

c)

d)

110.

a)

b)

c)

d)

111.

a)

b)

c)

d)

112.

How must the domain of f(x) be restricted such that g(x)=f^-1(x) ?

a)

x ≤ 0

b)

x ≥ 0

c)

x ≤ 3

d)

x ≥ 3

113.

How must the domain of f(x) be restricted such that g(x)=f^-1(x) ?

a)

x ≤ -4

b)

x ≥ -4

c)

x ≤ 0

d)

x ≥ 0

114.

a)

b)

c)

d)

115.

Which graph represents the functions f(x) and f^-1(x)?

a)

b)

c)

d)

116.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

117.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

118.

Which expression represents g(f(x)) if f(x) = 2x - 8
and
g(x) = 4x

a)

8x - 32

b)

8x² - 32x

c)

8x - 8

d)

6x - 8

119.

a)

9 - √17

b)

4

c)

2

d)

√8

120.

What is the inverse of this function?

a)

A

b)

B

c)

C

d)

D

121.

The composition of any function, f(x), and
its inverse, f^-1(x) =

a)

x

b)

f(x)

c)

1

d)

0

122.

Find the inverse of f(x) = x² - 5

a)

f^-1(x) = √(x) + 5

b)

f^-1(x) = ∛(x-5)

c)

f^-1(x) = ±√(x+5)

d)

f^-1(x) = x² - 5

123.

Which expression represents g(f(x)) if f(x) = 2x - 8
and
g(x) = 4x

a)

8x - 32

b)

8x² - 32x

c)

8x - 8

d)

6x - 8

124.

a)

A

b)

B

c)

C

d)

D

125.

a)

A

b)

B

c)

C

d)

D

126.

Given f(x)= -3x+7 and g(x)=2x² - 8, find g(f(x)).

a)

g(f(x))= -6x²+31

b)

g(f(x))= -6x²+24

c)

g(f(x))=18x²-84x+90

d)

g(f(x))=9x²-42x-41

127.

Are the following inverses of each other?

a)

True

b)

False

128.

Was the inverse function found correctly?

a)

no,

b)

yes

129.

What is the inverse of the points (1,3)(2,4)(6,2)

a)

(2,6)(3,1)(4,2)

b)

(-3,-1)(-4,-2)(-2,-6)

c)

(1,3)(2,4)(6,2)

d)

(-1,-3)(-2,-4)(-6,-2)

130.

Find the inverse
f(x)= x⁴- 2

a)

∜(x+2)

b)

(x+2)⁴

c)

-1+2x⁴

d)

∜2x

131.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

132.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = - 4x - 3

133.

When finding the inverse of a relation,
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

a)

solve for y

b)

replace y with f^-1(x)

c)

solve for x

d)

find the greatest common factor

134.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 1/4x + 7/4

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

135.

Given that f(x) = 3x + 5 and g(x) = 1/3x + 5, find f(g(x)). Are the two functions inverses of each other?

a)

x + 20 ; Yes they are inverses

b)

x + 20 ; No, they are not inverses

c)

x ; Yes they are inverses

d)

x ; No, they are not inverses

136.

Are the following inverses of each other? Use composition of functions. fog(x) and gof(x)

a)

True

b)

False

137.

f(x) = 3x + 10

g(x) = ⅓x - 3

Find g(f(x))

a)

f(g(x)) = 1

b)

f(g(x)) = x

c)

f(g(x)) = 0

d)

None of these.

138.

a)

Inverse Functions

b)

Not Inverse Functions

139.

a)

Inverse Functions

b)

Not Inverse Functions

140.

What operation allows us to verify if functions are inverses?

a)

Multiplying

b)

Dividing

c)

Adding

d)

Composing

141.

What does an inverse function do?

a)

Nothing

b)

Makes it bigger

c)

Does the opposite of the original function

142.

$f\left(x\right)=\frac{x-2}{6}$
Find $f^{-1}\left(x\right)$

a)

$\frac{x-6}{2}$

b)

$6x+2$

c)

$2x+6$

d)

$6\left(x+2\right)$

143.

$f\left(x\right)=\frac{8x-3}{5}$
Find $f^{-1}\left(x\right)$

a)

$5\left(8x+3\right)$

b)

$\frac{5x}{8}+3$

c)

$\frac{5\left(x+3\right)}{8}$

d)

$\frac{5x+3}{8}$

144.

$f\left(x\right)=\frac{6x}{5}+3$
Find $f^{-1}\left(x\right)$

a)

$\frac{5x-3}{6}$

b)

$\frac{5\left(x-3\right)}{6}$

c)

$\frac{5x}{6}-3$

d)

$\frac{5x}{6}+3$

145.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

146.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

a)

182

b)

40

c)

61

d)

None of the Above

147.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

148.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(x))

a)

3x + 8

b)

3x - 2

c)

3x + 4

d)

None of these.

149.

Find f(2).

a)

-2

b)

-18

c)

24

d)

6

150.

Find g(5)

a)

3375

b)

375

c)

25

d)

45

151.

f(x-2)

a)

2x² - 13x + 18

b)

2x² - 5x + 18

c)

2x² - 8x + 3

d)

2x² - 13x + 2

152.

g(4x)

a)

1728x³

b)

12x³

c)

192x³

d)

36x³

153.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

154.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

155.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

156.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

a)

182

b)

40

c)

61

d)

None of the Above

157.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

a)

16

b)

4

c)

-4

d)

None of these.

158.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

159.

g(a) = 4a + 1

h(a) = -3a + 2

Find g(h(1))

a)

3

b)

-3

c)

21

d)

-21

160.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(x))

a)

3x + 8

b)

3x - 2

c)

3x + 4

d)

None of these.

161.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

162.

If f(x) = x-1 and g(x) = 2x,

what is and g(f(x)) ?

a)

2x²-1

b)

2x-1

c)

2x-2

d)

x-2

163.

f(n)=2n+1
g(n)=3n
Find f(n)+g(n)

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

164.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

165.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(-1\right)\right)$

a)

2

b)

15

c)

7

d)

-9

166.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

167.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

168.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(f\circ g\right)\left(2\right)$

a)

$\frac{1}{4}$

b)

$\frac{1}{8}$

c)

$\frac{7}{2}$

d)

8

169.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ g\right)\left(-4\right)$

a)

44

b)

-40

c)

-30

d)

-28

170.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ f\right)\left(x\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

171.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $f\left(g\left(x\right)\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

172.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\sqrt{x}$ find $g\left(f\left(x\right)\right)$

a)

$x^4$

b)

$x$

c)

$\sqrt[]{x}$

d)

$x^2$

173.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\frac{1}{x^2}$ find $\left(f\circ g\right)\left(-1\right)$

a)

$\frac{1}{4}$

b)

$1$

c)

$-1$

d)

$-\frac{1}{4}$

174.

When $f(x)=x^2+9$ and $g(x)=x-9$ , find $f(x)-g(x)$

a)

$x^2+x+9$

b)

$x^2-x+9$

c)

$x^2-x$

d)

$x^2-x+18$

175.

When $f(x)=9-3x$ and $g(x)=5x-7$ , find $f(x)+g(x)$

a)

$14x-10$

b)

$-8x+2$

c)

$2x+2$

d)

$2x-2$

176.

$f\left(g\left(3\right)\right)$ (just give the final value)

(a)

177.

$g(h(-4))$ (just give the final value)

(a)

178.

$f\left(g\left(5\right)\right)$ (just give the final value)

(a)

179.

If $g\left(x\right)=x^2+6$ and $f\left(x\right)=2x-4$ , find $g\left(f\left(x\right)\right)$

a)

$2x^2-12x-4$

b)

$2x^2+12x-4$

c)

$4x^2-16x+22$

d)

$x^3-2x^2+1$

180.

a)

7

b)

6

c)

11

d)

None of the Above

181.

$g\left(f\left(2\right)\right)$

a)

5

b)

3

c)

-1

d)

2

182.

If $f\left(x\right)=2x+3$ and $g\left(x\right)=-3x-4$ , find $f\left(x\right)\cdot g\left(x\right)$

a)

$-6x^2-17x-12$

b)

$6x^2+x-12$

c)

$-x-1$

d)

$5x+7$

183.

$g\left(g\left(-5\right)\right)$

a)

1

b)

-0.25

c)

3

d)

-1

Composition and Inverse Functions

Total questions: 183

Worksheet time: 13hrs 32mins

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