Free Printable Composite of Functions

1.

Which one is the same as fοg(x)

a)

g(f(x))

b)

f(g(x))

2.

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

a)

19

b)

23

c)

-10

d)

None of these.

3.

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

a)

16

b)

4

c)

-4

d)

None of these.

4.

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

a)

-42

b)

-26

c)

-18

d)

None of these.

5.

What is f(g(3))?

a)

1/8

b)

8

c)

1/4

d)

1/2

6.

a)

9 - √17

b)

4

c)

2

d)

√8

7.

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

8.

Given $f\left(x\right)=3x-6$ and $g\left(x\right)=x^2+4$ , find $\left(g\circ f\right)\left(-1\right)$

a)

13

b)

85

c)

9

d)

65

9.

Given $f\left(x\right)=\sqrt{4x-4}$ and $g\left(x\right)=3x+1$ , find $\left(f\circ g\right)\left(3\right)$ in simplest form.

a)

-12

b)

6

c)

$2\sqrt{2}$

d)

$\sqrt{34}$

10.

Find f(h(5)) based on the graphs of f(x) and g(x)

a)

-6

b)

-3

c)

6

d)

2

11.

Given j(x) = ∛(x-1)
and h(x) = x³+1,
find j(h(x)).

a)

x³+3x²-9x-3

b)

x

c)

x³-3x²+3x-1

d)

j(x) * h(x)

12.

$h\left(x\right)=\left(x-3\right)^2$ and $g\left(x\right)=\sqrt{x-7}$
Find $h\left(g\left(11\right)\right)$

(a)

13.

If f(x) = 1/x and g(x) = x - 10, what is the domain of f(g(x))?

a)

{x | x not equal to 0}

b)

{x | x not equal to -10}

c)

{x | x not equal to 10}

d)

{x | x is all real numbers}

14.

What is the domain of f(g(x))?

a)

{x | x is not equal to -1, -2}

b)

{x | x is not equal to -1, -3}

c)

{x | x is not equal to -2, -3}

d)

{x | x is not equal to -1, -2, -3}

15.

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

(a)

16.

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

a)

-7

b)

-4

c)

0

d)

2

17.

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

(a)

18.

The table below shows the values of f(x) at selected values of x. The function g(x) is shown in the graph below. Find f(g(-2)).

a)

3

b)

5

c)

0

d)

10

Composite of Functions

Total questions: 18

Worksheet time: 28mins

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