Free Printable Quiz bank on composition of functions and inverses

1.

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

a)

14x-10

b)

-8x+2

c)

2x+2

d)

2x-2

2.

Given the functions

$f\left(x\right)=3x-9$ and $g\left(x\right)=x-11$ find $f+g$

a)

$4x-20$

b)

$3x^2-42x+99$

c)

$2x+2$

d)

$-2x-2$

3.

Given the functions

$f\left(x\right)=3x-9$ and $g\left(x\right)=x-11$ find $\frac{g}{f}$

a)

$\frac{3x-9}{x-11}$

b)

$\frac{x-11}{3x-9}$

c)

$\frac{3x}{x}$

d)

$\frac{9}{11}$

4.

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

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

5.

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

a)

-42

b)

-26

c)

-18

d)

None of these.

6.

are these inverse functions?

a)

no

b)

yes

c)

no way to tell

7.

Use the horizontal line test to determine whether the inverse of the graph is a function.

a)

Function

b)

Not a Function

8.

are these inverse functions?

a)

no

b)

yes

c)

no way to tell

9.

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

10.

Find the inverse of $f\left(x\right)=3x+2$

a)

$f^{-1}\left(x\right)=\frac{x-2}{3}$

b)

$f^{-1}\left(x\right)=\frac{x-3}{2}$

c)

$f^{-1}\left(x\right)=\frac{3x}{2}$

d)

$f^{-1}\left(x\right)=\frac{2+x}{3}$

11.

Find the inverse of $f\left(x\right)=-\frac{5}{8}x+10$

a)

$f^{-1}\left(x\right)=-\frac{8}{5}x-10$

b)

$f^{-1}\left(x\right)=10\left(x-\frac{8}{5}\right)$

c)

$f^{-1}\left(x\right)=-\frac{5}{8}\left(x-10\right)$

d)

$f^{-1}\left(x\right)=-\frac{8}{5}\left(x-10\right)$

12.

Find the inverse of $f\left(x\right)=x^2-4$

a)

$f^{-1}\left(x\right)=\sqrt{x+16}$

b)

$f^{-1}\left(x\right)=\sqrt{x-4}$

c)

$f^{-1}\left(x\right)=\sqrt{x}+4$

d)

$f^{-1}\left(x\right)=\sqrt{x+4}$

13.

Find the inverse of $f\left(x\right)=\sqrt{x-2}$

a)

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

b)

$f^{-1}\left(x\right)=x^2+2$

c)

$f^{-1}\left(x\right)=\left(x+2\right)^2$

d)

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

14.

(f + g) (x)

a)

5x² + 3x

b)

4x² + 3x

c)

5x² - 3x

d)

4x² - 40x

15.

(g- f)(x)

a)

5x² + 3x

b)

-3x² - 13x

c)

3x² + 11x

d)

-3x² + 3x

16.

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

a)

-26

b)

-18

c)

22

d)

8

17.

Find $\left(f\cdot g\right)\left(-2\right)$

a)

3375

b)

-432

c)

-205

d)

450

18.

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

a)

14x-10

b)

-8x+2

c)

2x+2

d)

2x-2

19.

If $f\left(x\right)=x^2+9$ and $g\left(x\right)=x-9$ . Find $f\left(x\right)-g\left(x\right)$

a)

$x^2+x$

b)

$x^2-x$

c)

$x^3-x^2-x+18$

d)

$x^2-x+18$

20.

$f\left(x\right)=4x+1\ and\ g\left(x\right)=4x-3.\ Find\ f\left(x\right)\cdot g\left(x\right)$

a)

$16x^2+8x-3$

b)

$16x^2-8x+3$

c)

$16x^2-8x-3$

d)

$16x^2-16x-3$

21.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

22.

Given $f\left(x\right)=x^2+5\ and\ g\left(x\right)=2x^3-1$ , find $\left(\frac{f}{g}\right)\left(-3\right)$ .

a)

-14/55

b)

14/55

c)

2

d)

-2

23.

Given g(x) = -2x+2 and f(x) = 3x²+4, find (g+f)(-3).

a)

39

b)

-27

c)

-23

d)

-19

24.

Given f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

25.

f(x) = 4x+8
g(x) = x+3,
Find f(x) * g(x)

a)

4x²+24

b)

4x²+20x+24

c)

4x²+12x+24

d)

4x²+4x+24

26.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

27.

f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f - g)(x).

a)

x² + 8x + 1

b)

x² + 6x - 1

c)

5x² + 8x - 1

d)

x² + 8x -1

28.

Given f(x) = 3x² - 2x + 1 and g(x) = x - 4, find (f⋅g)(x).

a)

3x³ - 10x² - 7x - 4

b)

3x³ - 14x² + 9x - 4

c)

3x² - x - 3

d)

3x³ + 14x² - 9x - 4

29.

Given the functions

$f\left(x\right)=3x-9$ and $g\left(x\right)=x-11$ find $f+g$

a)

$4x-20$

b)

$3x^2-42x+99$

c)

$2x+2$

d)

$-2x-2$

30.

Given the functions

$f\left(x\right)=3x-9$ and $g\left(x\right)=x-11$ find $f-g$

a)

$4x-20$

b)

$3x^2-42x+99$

c)

$2x+2$

d)

$-2x-2$

31.

Given the functions

$f\left(x\right)=3x-9$ and $g\left(x\right)=x-11$ find $g-f$

a)

$4x-20$

b)

$3x^2-42x+99$

c)

$2x+2$

d)

$-2x-2$

32.

Given the functions

$f\left(x\right)=3x-9$ and $g\left(x\right)=x-11$ find $g\times f$

a)

$4x-20$

b)

$3x^2-42x+99$

c)

$2x+2$

d)

$-2x-2$

33.

Given the functions

$f\left(x\right)=3x-9$ and $g\left(x\right)=x-11$ find $\frac{g}{f}$

a)

$\frac{3x-9}{x-11}$

b)

$\frac{x-11}{3x-9}$

c)

$\frac{3x}{x}$

d)

$\frac{9}{11}$

34.

Given the functions

$f\left(x\right)=x^2+5$ and $g\left(x\right)=4x-9$ find $f+g$

a)

$x^2+4x-4$

b)

$4x^3-9x^2+20x-45$

c)

$x^2-4x+14$

d)

$-x^2+4x-14$

35.

Given the functions

$f\left(x\right)=x^2+5$ and $g\left(x\right)=4x-9$ find $f-g$

a)

$x^2+4x-4$

b)

$4x^3-9x^2+20x-45$

c)

$x^2-4x+14$

d)

$-x^2+4x-14$

36.

Given the functions

$f\left(x\right)=x^2+5$ and $g\left(x\right)=4x-9$ find $g-f$

a)

$x^2+4x-4$

b)

$4x^3-9x^2+20x-45$

c)

$x^2-4x+14$

d)

$-x^2+4x-14$

37.

Given the functions

$f\left(x\right)=x^2+5$ and $g\left(x\right)=4x+9$ find $\frac{f}{g}$

a)

$\frac{4x-9}{x^2+5}$

b)

$\frac{x^2+5}{4x-9}$

c)

$\frac{x^2}{4x+9}$

d)

$-\ \frac{5}{9}$

38.

Simplify by combining like terms:

5a + 2b - 3a + 4

a)

8a + 2b + 4

b)

2a + 2b + 4

c)

8ab

d)

4ab + 4

39.

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

40.

When f(x) = 4x+8 and
g(x) = x+3, find
f(x) * g(x).

a)

4x²+24

b)

4x²+20x+24

c)

4x²+12x+24

d)

4x²+4x+24

41.

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

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

42.

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

43.

f(x)=2x+4
g(x)=3x²-1
Find f(x)*g(x)

a)

6x⁴+12x³-4x²-8x

b)

-6x³+12x²+2x-4

c)

6x³+12x²-2x-4

d)

5x²-18x+20

44.

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

a)

(x+3)/(x-2)

b)

(x-2)/(x+3)

c)

-2/3

d)

3/2

45.

h(x) = 3x + 3

g(x) = -4x + 1

Find (h + g)(10)

hint: add h(x) and g(x), then plug in 10

a)

-6

b)

6

c)

82

d)

-72

46.

g(x) = 2x - 5

h(x) = 4x + 5

Find (g - h)(3)

hint: subtract g(x) and h(x), then plug in 3

a)

18

b)

16

c)

-16

d)

28

47.

g(x) = 2x - 5

h(x) = 4x + 5

Find (g - h)(3)

hint: subtract g(x) and h(x), then plug in 3

a)

18

b)

16

c)

-16

d)

28

48.

Find (f + g)(x)

a)

2x² - 3

b)

9

c)

x⁴ - 3x² - 18

d)

(x² + 3)/(x² -6)

49.

Find (fg)(x)

a)

x² - 3

b)

9

c)

x⁴ - 3x² - 18

d)

(x² + 3)/(x² - 6)

50.

Find (f/g)(x)

a)

x² - 3

b)

3/-6

c)

x⁴ - 3x² - 18

d)

(x² + 3)/(x² - 6)

51.

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

a)

-4

b)

-2

c)

0

d)

4

52.

Find $f\left(g\left(4\right)\right)$

a)

1

b)

-2

c)

-3

d)

-4

53.

Find $g\left(f\left(6\right)\right)$

(a)

54.

Find $g\left(f\left(1\right)\right)$

a)

-7

b)

-1

c)

0

d)

2

55.

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

(a)

56.

a)

9 - √17

b)

4

c)

2

d)

√8

57.

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

a)

19

b)

23

c)

-10

d)

None of these.

58.

Evaluate f(2):

f(x)=3x+1

a)

7

b)

9

c)

11

d)

13

59.

Find the inverse for this relation: { (1, -3), (-2, 3), (5, 1), (6, 4) }

a)

{ (1, 3), (2, 3), (5, 1), (6, 4) }

b)

{ (-1, -3), (-2, -3), (-5, -1), (-6, -4) }

c)

{ (3, -1), (-3, 2), (-5, 1), (4, -6) }

d)

{ (-3, 1), (3, -2), (1, 5), (4, 6) }

60.

Find the inverse: f(x) = 3x + 2

a)

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

b)

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

c)

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

d)

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

61.

If f(x) = 3x-1 and g(x) = x²+2,

what is (f ° g)(x) ?

a)

3x² +5

b)

x² +1

c)

3x² +1

d)

3x² +6

62.

If f(x) = 5x and g(x) = 2x-1,

what is the composition f(g(x)) ?

a)

10x-1

b)

10x-5

c)

5x²-1

d)

5x²-5

63.

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

64.

Find f(- 3).

a)

33

b)

-2

c)

-24

d)

18

65.

g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

66.

f(x) = 3x + 10

g(x) = x - 2

Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

67.

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

68.

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

69.

Given f and g in the graph,

what is (f ° g)(-1) ?

a)

1

b)

4

c)

-1

d)

6

70.

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)

71.

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

72.

Was the inverse function found correctly?

a)

no,

b)

yes

73.

Find the inverse of the function
f(x) = 3x − 5

a)

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

b)

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

c)

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

d)

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

74.

Find the inverse function

a)

b)

c)

d)

75.

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

a)

f^-1(x)= $\frac{x+2}{2}$

b)

f^-1(x)= $\frac{2}{x+2}$

c)

f^-1(x)= $\frac{2x}{x-2}$

d)

f^-1(x)= $\frac{2y}{x-2}$

76.

$g\left(x\right)=\frac{x}{9}$ Find $g^{-1}\left(x\right)$

a)

$\frac{8}{x}$

b)

$9x$

c)

$\frac{1}{8}x$

d)

$x\div8$

77.

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

78.

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)

79.

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

80.

Find the inverse
f(x)= x⁴- 2

a)

∜(x+2)

b)

(x+2)⁴

c)

-1+2x⁴

d)

∜2x

81.

The inverse has been reflected over which line?

a)

y = x

b)

x = 0

c)

y = 0

d)

x = -y

82.

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.

83.

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.

84.

A function has an inverse if: f(g(x) = x

a)

True

b)

True, if x = 1

c)

True, if g(f(x) = x

d)

False, an inverse never = x

85.

Are f(x) = 4x-7 and g(x) = (x+7)/4 inverses of each other?

a)

No

b)

Yes, but only if x is not equal to -7

c)

Yes, or all x > -4

d)

Yes

86.

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

87.

What is the inverse of the points
(1,3)(2,4)(6,8)

a)

(3,1)(4,2)(8,6)

b)

(-3,-1)(-4,-2)(-8,-6)

c)

(1,3)(2,4)(6,8)

d)

(-1,-3)(-2,-4)(-6,-8)

88.

In an inverse function, the _____ and _______ are switched from the original

a)

f(x) and g(x)

b)

input and output

c)

positives and negatives

d)

slope and intercept

89.

(f - g) (x)

a)

5x² + 3x

b)

-3x² - 13x

c)

5x² - 3x

d)

4x² - 40x

90.

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

a)

$\frac{1}{11}$

b)

$\frac{1}{8}$

c)

$\frac{7}{2}$

d)

8

91.

Given g(x) = -2x+2 and f(x) = 3x²+4, find (g+f)(-2).

a)

39

b)

-27

c)

22

d)

-19

92.

Given g(x) = -2x+3 and f(x) = 3x²+4, find (g+f)(-2).

a)

39

b)

-27

c)

22

d)

23

93.

g(x)=3x+4 h(x)=3x-1 Find (h∘g)(x)

a)

-9x+11

b)

4x²+4x

c)

9x+11

d)

9x+11

94.

Find $f\left(g\left(-1\right)\right)$

a)

-1

b)

0

c)

4

d)

1

95.

(f - g) (2)

a)

-38

b)

36

c)

26

d)

-8

96.

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

97.

Find the inverse f(x)=3x-2

a)

f^-1(x)= $\frac{x+3}{3}$

b)

f^-1(x)= $\frac{x+2}{3}$

c)

f^-1(x)= $\frac{x-2}{3}$

d)

$f^{-1}\left(y\right)=3y-4$

98.

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

a)

34

b)

71

c)

35

d)

14

99.

When f(x) =3x+8 and g(x) = 2x+3, find f(x) * g(x).

a)

5x²+24

b)

6x²+25x+24

c)

6x²+12x+24

d)

5x²+4x+24

100.

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)

Quiz bank on composition of functions and inverses

Total questions: 100

Worksheet time: 8hrs 20mins

Similar Resources on Wayground