Free Printable Function Inverse and Operations Review

1.

How are you today?

a)

😁

b)

😒

c)

😴

d)

😐

2.

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

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

3.

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

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

4.

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.

5.

If f(x)=x+5, what is f^-1(x)?

a)

(x + 5)²

b)

x - 5

c)

(x + 5)^-1

d)

undefined

6.

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

7.

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

8.

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

9.

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

a)

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

b)

$6x+2$

c)

$2x+6$

d)

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

10.

F(x) = x + 11

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

a)

S1: let F(x) = x + 11

S2: Interchange x <=> y

x = y + 11

S3: Solve for y

11x = y

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

b)

S1: let y = x + 11

S2: Solve for x

x = y + 11

S3: Interchange x <=> y

x + 11 = y

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

c)

S1: let y = x + 11

S2: Solve for x

y + 11 = x

S3: Interchange x <=> y

y = x - 11

S4: F(x) = x

d)

S1: let y = x + 11

S2: Solve for x

y+ 11 = x

S3: Interchange x <=> y

y = x - 11

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

11.

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)

$16x^2-16x-3$

12.

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)

$x^2-2x-4$

13.

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)

$5x^2+8x-1$

14.

When f(x) = x²- 9

and g(x) = x - 3 ,

find f(x) / g(x).

a)

$x+3$

b)

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

c)

$\frac{x^2-9}{x-3}$

d)

$\frac{\left(x-3\right)\left(x+3\right)}{x-1}$

15.

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)

$x^2-x+18$

16.

Evaluate f(t)=-2t²+ 1 for f(-3)

a)

19

b)

37

c)

-17

d)

-11

17.

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

a)

7

b)

-2

c)

-9

d)

-10

18.

f(x) = 3x² - 4x + 5

g(x) = 5x - 1

Find (f ⋅ g)(x).

a)

15x³ - 23x² + 29x - 5

b)

15x³ - 4x - 5

c)

15x³ + 4x + 5

d)

15x³ + 23x² - 29x - 5

19.

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)

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

d)

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

20.

p(x) = 3x + 4
q(x) = 2x²
Find q(p(-2))

a)

8

b)

-8

c)

28

d)

None of these.

21.

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

Function Inverse and Operations Review

Total questions: 21

Worksheet time: 1hrs 11mins

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