Free Printable Function Operations, Composition, Inverse

1.

If $f(x)=4x+1$ and $g(x)=4x-3$

Find $f(x)*g(x)$

a)

$16x^2+8x-3$

b)

$16x^2-8x+3$

c)

$16x^2-8x-3$

d)

$16x^2-16x-3$

2.

If $f(n)=x^2+1$ and $g(n)=2x-5$ Find $f(n)-g(n)$

a)

$x^2-2x+6$

b)

$-x^2+2x+4$

c)

$-x^2-2x-6$

d)

$x^2-2x-4$

3.

If $f(x)=3x^2+7x$ and $g(x)=2x^2-x-1$ ,

find $(f+g)(x)$ .

a)

$11x^2-1$

b)

$5x^4+6x^2-1$

c)

$5x^2+6x-1$

d)

$5x^2+8x-1$

4.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

5.

If $f(x)=x^2+9$ 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)

$x^2-x+18$

6.

All possible y values are known as _________

a)

Domain

b)

Range

c)

Relation

d)

Function

7.

Complete the operation and evaluate.

a)

b)

c)

d)

8.

What is the definition of a function?

a)

Has inputs and outputs

b)

Inputs have different outputs every time

c)

x-values and

y-values

d)

Every input has only one output

9.

If f(x) = -4x - 5 and
g(x) = 3 - x,
what is g(-4) + f(1)?

a)

7

b)

-2

c)

-9

d)

-10

10.

a)

A

b)

B

c)

C

d)

D

11.

a)

A

b)

B

c)

C

d)

D

12.

a)

A

b)

B

c)

C

d)

D

13.

a)

A

b)

B

c)

C

d)

D

14.

Find the inverse of g(x).

a)

A

b)

B

c)

C

d)

D

15.

Find the inverse of f(x). Then graph f(x) and its inverse.

a)

A

b)

B

c)

C

d)

D

16.

f(x)= x+3

g(x)= x-2

Find (g(x) / f(x))

Be careful!!

a)

(x + 3)/(x - 2)

b)

(x - 2)/(x + 3)

c)

-2/3

d)

3/2

17.

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

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

18.

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

a)

f(g(x))= -6x²+31

b)

f(g(x))= -6x²+24

c)

f(g(x))=18x²-84x+6

d)

f(g(x))=9x²-42x-1

19.

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

20.

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

a)

-42

b)

-26

c)

-18

d)

None of these.

21.

f(x)= x²- 1

g(x)= x - 1

Find (f(x)/g(x))

Then simplify using x = 10

a)

9

b)

11

c)

90

d)

110

22.

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

a)

19

b)

23

c)

-10

d)

None of these.

23.

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

a)

16

b)

4

c)

-4

d)

None of these.

24.

p(x) = 3x + 4
q(x) = 2x²
Find p(q(x))

a)

10x²

b)

18x² + 4

c)

6x² + 4

25.

Given f(x) = -x + 4 and g(x) = 6x + 3, find (f - g)(x).

a)

-7x + 1

b)

5x +1

c)

-5x -1

d)

5x + 1

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.

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

28.

Find the inverse of $f\left(x\right)=\frac{1}{4}x-7$

a)

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

b)

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

c)

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

d)

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

29.

a)

Inverse Functions

b)

Not Inverse Functions

30.

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

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

31.

F(x) = 11x

Then use 4 step to find inverse F^-1(x)

a)

S1: let F(x), x = 11y

S2: Interchange x <=> y

y = 11x

S3: Solve for y

y = x

S4: F(x)^-1 = x

b)

S1: let y = x + 11

S2: Interchange x <=> y

x = 11y

S3: Solve for y

y = 11x

S4: F(x)^-1 = 11x

c)

S1: let y = 11x

S2: Interchange x <=> y

x = 11y

S3: Solve for y

x/11 = y

S4: F(x)^-1 = x/11

d)

S1: let y = 11x

S2: Interchange x <=> y

x = 11y

S3: Solve for y

11/x = y

S4: F(x) = 11/x

32.

The inverse has been reflected over which line?

a)

y = x

b)

x = 0

c)

y = 0

d)

x = -y

33.

Find the domain and range of the INVERSE of the following function

a)

Domain: {-2, -1, 1, 8}

Range: {2, 3, 5}

b)

Domain: {2, 3, 5}

Range: {-2, -1, 1, 8}

c)

Domain: {-1, 8, 1, -2}

Range: {3, 2, 3, 5}

d)

Domain: {3, 2, 3, 5}

Range {-1, 8, 1, -2}

34.

Graph the inverse

a)

b)

c)

d)

35.

If this is the table for f(x), what is the correct table for f^-1(x)?

a)

b)

c)

d)

36.

Are these the graphs of two inverse functions?

a)

Yes

b)

No

c)

No way to tell

37.

Which of the following is the inverse function for ? $f\left(x\right)\ =\ \frac{x^2+\ 1}{4}$

a)

$f^{-1}\left(x\right)\ =\ \left(4x\ +\ 1\right)^2$

b)

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

c)

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

d)

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

38.

If f(x) and g(x) are inverse functions, which statements are true?

SELECT ALL THAT APPLY.

a)

f(x) and g(x) are reflection images over y=x

b)

The domain of f is the range of g and vice versa.

c)

f(g(x)) = g(f(x)) = x

d)

The functions are equivalent.

39.

Find the inverse function

a)

b)

c)

d)

40.

Find the inverse function

a)

b)

c)

d)

41.

Find the inverse function

a)

b)

c)

d)

42.

Is the inverse function found correctly?

a)

yes

b)

no

43.

G(x) = $\sqrt[]{x}$ . Find G^-1(x)

a)

S1: Let y = $\sqrt[]{x}$

S2: x <=> y

x = $\sqrt[]{y}$

S3: solve for y

x² = y

S4: y = G(x)^-1 = x²

b)

S1: Let y = x²

S2: x <=> y

x = y²

S3: solve for y

$\sqrt[]{x}$ = y

S4: y = G(x)^-1 = $\sqrt[]{x}$

c)

S1: Let y = $\sqrt[]{x}$

S2: x <=> y

x = $\sqrt[]{y}$

S3: solve for y

x - 2 = y

S4: y = G(x)^-1 = x - 2

d)

S1: Let y = $\sqrt[]{x}$

S2: x <=> y

x = $\sqrt[]{y}$

S3: solve for y

x = y

S4: y = G(x)^-1 = x

44.

G(x) = 4x³ - 1. Find G^-1(x)

a)

S1: Let

y = 4x³- 1

S2: x <=> y

x = 4y³- 1

S3: solve for y

$\left(\frac{x+1}{4}\right)^3$ = y

S4: G(x)^-1 = $\left(\frac{x+1}{4}\right)^3$

b)

S1: Let

y = 4x³- 1

S2: x <=> y

x = 4y³- 1

S3: solve for y

(x³ - 1)/4= y

S4: G(x)^-1 = (x³ - 1)/4

c)

S1: Let

y = 4x³- 1

S2: x <=> y

x = 4y³- 1

S3: solve for y

$\sqrt[3]{\frac{x+1}{4}}$ = y

S4: G(x)^-1 = $\sqrt[3]{\frac{x+1}{4}}$

d)

S1: Let

y = 4x³- 1

S2: x <=> y

x = 4y³- 1

S3: solve for y

4x³ + 1 = y

S4: G(x)^-1 = 4x³ + 1

45.

G(x) = $\sqrt[]{x}$ + 1. Find G^-1(x)

a)

S1: Let y = $\sqrt[]{x}$ + 1

S2: x <=> y

x = $\sqrt[]{y}$ + 1

S3: solve for y

(x-1)² = y

S4: G(x)^-1 = x² - 1

b)

S1: Let y = $\sqrt[]{x}$ + 1

S2: x <=> y

x = y² + 1

S3: solve for y

$\sqrt[]{x}$ - 1 = y

S4: G(x)^-1 = $\sqrt[]{x}$ - 1

c)

S1: Let y = $\sqrt[]{x}$ + 1

S2: x <=> y

x = $\sqrt[]{y}$ + 1

S3: solve for y

x - 1 = y

S4: G(x)^-1 = x - 1

d)

S1: Let y = $\sqrt[]{x}$ + 1

S2: x <=> y

x = $\sqrt[]{y}$

S3: solve for y

$\left(x-\ 1\right)^2$ = y

S4: G(x)^-1 = $x^{2\ }-2x+1$

46.

Give the domain of $\frac{x+2}{x-2}$

a)

all real numbers except $-1$

b)

all real numbers except $1$

c)

all real numbers except $-2$

d)

all real numbers except $2$

47.

What value of x is restricted from the domain? $\frac{x^3}{3x+7}$

a)

$-7$

b)

$7$

c)

$-\frac{7}{3}$

d)

$-\frac{3}{7}$

e)

0

48.

$\frac{4xy}{x^2+9x+18}$

The domain of the rational algebraic expression above is:

a)

all real numbers except $-3\ \ \ \ \ and\ \ \ \ \ -6$

b)

all real numbers except $3\ \ \ \ and\ \ \ \ \ 6$

c)

all real numbers except $9\ \ \ \ and\ \ \ \ 2$

d)

all real numbers except $-9\ \ \ \ and\ \ \ -2$

49.

Given f(x)= 34x^4-727643x+1470789 and g(x)= 720x^30+13x-1789999, determine the domain of f(x) + g(x)

a)

x>958439630680863069

b)

All reals

c)

Woah that's a lot of numbers:/

d)

x=24 x=96

50.

Given f(x)=5x+4 and h(x)=-3x-3, what is the domain of f(x)+h(x)?

a)

All real numbers

b)

All real numbers, x≠-1/2

c)

2x+1

d)

8x+7

51.

If f(x)=3-x and g(x)=x+5, find the domain of f(x)/g(x)

a)

x is not equal to -5

b)

x is not equal to 3

c)

x is all real numbers

d)

x is equal to -5 and 3

52.

If $f(x)=\sqrt{x-3}$ , what is the domain?

a)

x=3

b)

x=-3

c)

x≥3

d)

x≤3

53.

Given $a(x)=-4x+5$ and $q\left(x\right)=x^2-5x+6$ , what is the domain of $\frac{a\left(x\right)}{q\left(x\right)}\$ ?

a)

All real numbers

b)

All real numbers, x≠5/4

c)

All real numbers, x≠3, x≠2

d)

All real numbers, x≠0, x≠3, x≠2

54.

Given f(x)=3x+7 and g(x)=8x-2, what is the domain of f(x)-g(x)?

a)

All real numbers

b)

All real numbers, x≠0

c)

All real numbers, x≠9/5

d)

All real numbers, x≠-5/11

55.

If f(x)= 27x+4, and g(x)= 36x+2, what is the domain of f(x)/g(x)?

a)

D: R, x can't equal -4/27

b)

D: R

c)

D: R, x can't equal -1/18

d)

D: R, x can't equal 36

Function Operations, Composition, Inverse

Total questions: 55

Worksheet time: 3hrs 15mins

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