Free Printable Test 6: Evaluating, Building, and Inverse Functions

1.

What's the name of the inverse of g(x)?

a)

f(x)

b)

f^-1(x)

c)

y

d)

g^-1(x)

2.

What is the inverse of the function
f(x) = 2x + 4 ?

a)

f^-1(x) = 4(x -2)

b)

f^-1(x) = (x-4)/2

c)

f^-1(x) = x/2 - 4

d)

f^-1(x) = x/4 + 2

3.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

4.

Are these functions inverses of each other?

a)

Yes

b)

No

5.

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)

6.

are these inverse functions?

a)

no

b)

yes

c)

no way to tell

7.

f(x) = {(3, 7), (4, -2), (5, -1), (8, 7)}
Is f^-1(x) a function?

a)

Yes

b)

No

c)

No way to tell

8.

Was the inverse function found correctly?

a)

no,

b)

yes

9.

are these inverse functions?

a)

no

b)

yes

c)

no way to tell

10.

a)

9

b)

3

c)

5

d)

√15

11.

a)

9 - √17

b)

4

c)

2

d)

√8

12.

a)

-1

b)

1

c)

-1/3

d)

-5/3

13.

If f(x)=2(3^x)+1, what is the value of f(2)?

(Substitute and be careful with order of operations)

a)

19

b)

37

c)

13

d)

20

14.

Evaluate f(2):

f(x)=3x+1

a)

7

b)

9

c)

11

d)

13

15.

If g(x)=2x+5, what is the value of g(4)?

(a)

16.

Given that h(x)=x³-2, evaluate h(4)

a)

62

b)

10

c)

64

d)

12

17.

Which of the following has the smallest value?

Let m(x)= $-3x+5$

a)

m(-1)

b)

m(0)

c)

m(1)

d)

m(2)

18.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

19.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

20.

What is the best description?

a)

They are both functions, but not inverse functions.

b)

They are inverse functions.

c)

They are reflected over y=x, but they are not both functions.

d)

They are not reflected over y=x, and they are not both functions.

21.

f(x) = -4x - 12

What is f^-1(x)?

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

22.

Which is f ^-1(x)?

a)

f^-1(x) = 5x + 3

b)

f^-1(x) = 5x - 3

c)

f^-1(x) = 5x - 15

d)

f^-1(x) = 1/5(x) + 3/5

23.

Which is f ^-1(x)?

a)

f^-1(x) = 3x + 5

b)

f^-1(x) = 3x - 5

c)

f^-1(x) = 3x - 15

d)

f^-1(x) = 3x + 15

24.

Which graph represents the functions f(x) and f^-1(x)?

a)

b)

c)

d)

25.

Which graph represents the functions f(x) and f^-1(x)?

a)

b)

c)

d)

26.

Find the inverse of $f(x)=2x+1$

a)

$f^{-1}(x)=2x$

b)

$f^{-1}(x)=\frac{x-1}{2}$

c)

$f^{-1}(x)=2$

27.

Find the inverse of $f(x)=4x$

a)

$f^{-1}(x)=\frac{x}{4}$

b)

$f^{-1}(x)=4$

c)

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

28.

Find the inverse of $f(x)=\frac{1}{x}$ .

a)

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

b)

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

c)

no solution

29.

f(n)=2n+1
g(n)=3n
Find f(n)+g(n)

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

30.

f(n)=x²+1
g(n)=2x-5
Find f(n)-g(n)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

31.

f(x)=x²+1
g(x)=2x-5
Find f(x)-g(x)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

32.

f(n)=2n+1
g(n)=3n
Find f(n)+g(n)

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

33.

f(n)=n²+4n
g(n)=-n-5
Find f(n)+g(n)

a)

n²+3n-5

b)

-n³+2n-7

c)

n³+3n-3n

d)

n²-3n-5

34.

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

35.

Which graph does NOT pass the vertical line test?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

36.

f(x) = 6x² + 3x + 2 and g(x) = x - 7

Find f(x) * g(x)

a)

6x³ - 39x² - 19x + 14

b)

6x³ - 39x² - 21x - 14

c)

6x³ - 39x² - 19x - 14

d)

6x³ - 45x² - 19x + 14

37.

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

a)

6x + 15

b)

6x - 15

c)

-6x + 15

d)

6x - 8

38.

f(x)=4x+1 g(x)=5x−2

Find (f $\cdot$ g)(x)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

39.

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

40.

f(x)=2x + 4

g(x)=3x²- 1

Find f(x) ⋅ g(x)

a)

6x⁴+ 12x³- 4x²- 8x

b)

-6x³+ 12x²+ 2x - 4

c)

6x³+ 12x²- 2x - 4

d)

5x²- 18x + 20

41.

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

42.

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

43.

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

a)

16

b)

4

c)

-4

d)

None of these.

44.

p(x) = 3x + 4

q(x) = 2x²

Find p(q(x))

a)

10x²

b)

18x² + 4

c)

6x² + 4

45.

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

46.

Perform the indicated operation.

a)

b)

c)

d)

47.

Perform the indicated operation.

a)

b)

c)

d)

48.

Complete the operation and evaluate.

a)

b)

c)

d)

49.

Perform the indicated operation.

a)

b)

c)

d)

50.

Perform the indicated operation.

a)

b)

c)

d)

51.

Given the functions

f\left(x\right)=x^2-3

and

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

find

g\circ f

a)

$\sqrt{x^2-8}$

b)

$x-8$

c)

$\sqrt{x^2+2}$

d)

$x-2$

52.

Given the functions

f\left(x\right)=x^2+1

and

g\left(x\right)=x-2

find

g\circ f

a)

$x^2-4x+5$

b)

$x^2-1$

c)

$x^3-2x^2+x-2$

d)

$x^2+x-1$

53.

Given the functions

f\left(x\right)=x^2+1

and

g\left(x\right)=x-2

find

f\circ g

a)

$x^2-4x+5$

b)

$x^2-1$

c)

$x^3-2x^2+x-2$

d)

$x^2+x-1$

54.

To say that something is commutative means that:

a)

You get the same answer forwards and backwards

b)

You always get x as an answer

c)

You are always adding the items

d)

You are always multiplying the items

55.

True or False:

Composition of Functions is commutative.

a)

True

b)

False

56.

g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

57.

If f(x) = x-5 and g(x) = 3x²-1,

what is (f ° g)(x) ?

a)

3x²-5

b)

3x²-1

c)

3x²-4

d)

3x²-6

58.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

59.

a)

b)

c)

d)

Test 6: Evaluating, Building, and Inverse Functions

Total questions: 59

Worksheet time: 3hrs 35mins

Similar Resources on Wayground