Free Printable Composite functions

1.

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

a)

19

b)

23

c)

-10

d)

None of these.

2.

What is f(g(3))?

a)

1/8

b)

8

c)

1/4

d)

1/2

3.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of g(f(-2)).

a)

-14

b)

20

c)

6

d)

7

4.

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

5.

If f(x) = x² and g(x) = 3x - 1, find f(g(x))

a)

9x² - 6x + 1

b)

3x - 1

c)

3x² - 1

d)

9x² - 1

6.

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

7.

Find h(g(x))

a)

2x + 6

b)

2x + 3

c)

2x² + 6

d)

2x² + 3

8.

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

9.

a)

9 - √17

b)

4

c)

2

d)

√8

10.

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=3+4x$ , find $\left(f\circ g\right)\left(x\right)$ in simplest form.

a)

$15+16x$

b)

$31+20x$

c)

$22+20x$

d)

$42+25x$

11.

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

a)

$9x^2-36x$

b)

$9x^2+42$

c)

$9x^2+36x-42$

d)

$9x^2-36+40$

12.

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

13.

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)

$\sqrt{34}$

14.

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

a)

$9x+4$

b)

$12x-2$

c)

$12x-6$

d)

$9x+3$

15.

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

a)

undefined

b)

-1

c)

0

d)

1

Composite functions

Total questions: 15

Worksheet time: 1hrs 15mins

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