Free Printable Operations on Functions and Inverse of a Function

1.

Evaluate f(t)=-2t²+1 for f(-3).

a)

19

b)

37

c)

-17

d)

-11

2.

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

3.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f-g\right)\left(x\right)=$

a)

-4x - 3

b)

-4x +1

c)

6x + 1

d)

6x - 3

4.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f\cdot g\right)\left(x\right)=$

a)

$5x-3$

b)

$5x^2+2$

c)

$5x^2-7x+2$

d)

$5x-7$

5.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(\frac{f}{g}\right)\left(x\right)$

a)

$\frac{x-1}{5x-2}$

b)

$\frac{5x-2}{x-1}$

c)

$\frac{-1}{3}$

d)

$-3$

6.

If $f\left(x\right)\ =\ 3x^2-4$ and $g\left(x\right)=x^2-8x+4$ , then $\left(f+g\right)\left(x\right)=$

a)

$4x^4-8x-8$

b)

$4x^4-8x$

c)

$4x^2-8x-8$

d)

$4x^2-8x$

7.

If $f\left(x\right)\ =\ 3x^2-4$ and $g\left(x\right)=x^2-8x+4$ , then $\left(f-g\right)\left(x\right)=$

a)

$2x^2-8x-8$

b)

$2x^2+8x-8$

c)

$2x^2-8x$

d)

$2x^2+8x$

8.

If $f\left(x\right)\ =\ 3x^2-4$ and $g\left(x\right)=x^2-8x+4$ , then $\left(f\cdot g\right)\left(x\right)=$ (Multiply)

a)

$3x^4-24x^3+8x^2+32x-16$

b)

$3x^4-8x-16$

c)

$3x^4-24x^3+8x^2-32x-16$

d)

$3x^4-24x^3+16x^2+32x-16$

9.

If $f\left(x\right)\ =\ 3x^2-4$ and $g\left(x\right)=x^2-8x+4$ , then $\left(\frac{f}{g}\right)\left(x\right)=$

a)

$\frac{3x^2-4}{x^2-8x+4}$

b)

$\frac{x^2-8x+4}{3x^2-4}$

c)

$\frac{3x^2-1}{x^2-8x}$

d)

$\frac{1}{-4x}$

10.

If $f\left(x\right)\ =\ x^2+6x-2$ and $g\left(x\right)=x-6$ , then $\left(f\circ g\right)\left(x\right)=$ ( Composition of functions and not a multiplication of functions)

a)

$x^2-6x+34$

b)

$x^2-6x-2$

c)

$x^2+6x-8$

d)

$x^2+6x-2$

11.

If $f\left(x\right)\ =\ x^2+6x-2$ and $g\left(x\right)=x-6$ , then $\left(g\circ f\right)\left(x\right)=$ ( Composition of functions and not a multiplication of functions)

a)

$x^2-6x+34$

b)

$x^2-6x-2$

c)

$x^2+6x-8$

d)

$x^2+6x+12$

12.

When 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

13.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

a)

182

b)

40

c)

61

d)

None of the Above

14.

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

a)

16

b)

4

c)

-4

d)

None of these.

15.

$Find\ f\left(8\right)\ if\ f\left(x\right)\ is\ given\ as\ described$

a)

0

b)

5

c)

11

d)

16

16.

Given $f\left(x\right)=3x^2-2x+1$ and $g\left(x\right)=x-4$ , find $\left(fg\right)\left(x\right)\ \ ->multiplication\ of\ functions$

a)

$3x^3-10x^2-7x-4$

b)

$3x^3-14x^2+9x-4$

c)

$3x^2-x-3$

d)

$3x^3+14x^2-9x-4$

17.

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

a)

-14/55

b)

14/55

c)

2

d)

-2

18.

Find the inverse of

f\left(x\right)\ =\ \sqrt{x-5}

a)

$f^{-1}\left(x\right)\ =\ x^2-\ 5$

b)

$f^{-1}\left(x\right)\ =\ x^2+5$

c)

$f^{-1}\left(x\right)\ =\ \left(x+5\right)^2$

d)

$f^{-1}\left(x\right)\ =\ \left(x\ -5\right)^2$

19.

$g\left(x\right)=\frac{4-\sqrt[3]{4x}^{ }}{2}$ Find the inverse of the function.

a)

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

b)

$g^{-1}\left(x\right)=-3-2x^5$

c)

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

d)

$g^{-1}\left(x\right)=-\frac{^3\sqrt{4x}}{2}$

20.

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)

21.

Are the following inverses of each other?

a)

True

b)

False

22.

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

23.

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

a)

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

b)

$6x+2$

c)

$2x+6$

d)

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

24.

$f\left(x\right)=\frac{8x-3}{5}$
Find $f^{-1}\left(x\right)$

a)

$5\left(8x+3\right)$

b)

$\frac{5x}{8}+3$

c)

$\frac{5\left(x+3\right)}{8}$

d)

$\frac{5x+3}{8}$

25.

Is the inverse function found correctly?

a)

yes

b)

no

26.

a)

Inverse Functions

b)

Not Inverse Functions

27.

Was the inverse function found correctly?

a)

no,

b)

yes

28.

Find the domain and range of the function
Hint: Use a scratch graph to help you visualize things.

a)

Domain: (-∞, ∞) Range: [-∞, 4]

b)

Domain: [1, ∞) Range: (-∞, 4]

c)

Domain: [-1. ∞) Range: [4, ∞)

d)

Domain: [4, ∞) Range: [-1,∞)

29.

Find the inverse of the following:

$\left\{\left(-1,0\right),\ \left(3,4\right),\ \left(5,\ -10\right)\right\}$

a)

$\left\{\left(0,1\right),\ \left(-4,\ -3\right),\ \left(10,-5\right)\right\}$

b)

$\left\{\left(1,0\right),\ \left(-3,\ -4\right),\ \left(-5,\ 10\right)\right\}$

c)

$\left\{\left(0,-1\right),\ \left(4,3\right),\ \left(-10,5\right)\right\}$

30.

Which of these graphs does NOT show inverse functions?

a)

b)

c)

d)

31.

Let $f\left(x\right)=x^2+1$ and $g\left(x\right)=-7x+2$ . Find $\left(g\ ∘\ f\right)\left(x\right)$ .

a)

$\left(g\ ∘\ f\right)\left(x\right)=-7x^2-5$

b)

$\left(g\ ∘\ f\right)\left(x\right)=3x^2-5$

c)

$\left(g\ ∘\ f\right)\left(x\right)=49x^2-28x+6$

32.

Using the table, find $g\left(f\left(-1\right)\right)$ .

(a)

33.

The inverse has been reflected over which line?

a)

y = x

b)

x = 0

c)

y = 0

d)

x = -y

34.

Which of the following is NOT TRUE about inverse functions?

a)

Inverse functions are reflections of each other over the line y = x.

b)

You find the inverse by switching x and y in the equation.

c)

The domain of a function always becomes the domain of its inverse.

d)

The domain of a function always becomes the range of its inverse.

35.

Find the inverse, $f^{-1}\left(x\right)$ , of $f\left(x\right)$
given $f\left(x\right)=x^2+7.$

a)

$\sqrt{x+7}$

b)

$\pm\sqrt{x+7}$

c)

$\pm\sqrt{x}-7$

d)

$\pm\sqrt{x-7}$

Operations on Functions and Inverse of a Function

Total questions: 35

Worksheet time: 2hrs 39mins

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