Function Inverses Date Period

Kuta Software - Infinite Algebra 2

Function Inverses

State if the given functions are inverses.

1)

g(x) = 4 -

3 x

2

f (x) = 1 x + 3

2 2

3) f (n) = -16 + n

4

g(n) = 4n + 16

5) f (n) = -(n + 1)3 g(n) = 3 + n3

7) f (x) = 4 + 2

-x - 2

h(x) = - 1

x + 3

Find the inverse of each function.

9)

h(x) =

3

x

- 3

Name___________________________________ Date________________ Period____

2) g(n) = -12 - 2n

3

f (n) = -5 + 6n

5

4) f (x) = - 4 x - 16

7 7

g(x) = 3 x - 3

2 2

6) f (n) = 2(n - 2)3

3

g(n) = 4 + 4n

2

8) g(x) = - 2 - 1

x

f (x) = - 2

x + 1

10) g(x) = 1 - 2

x

11) h(x) = 2x3 + 3

12) g(x) = -4x + 1

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Worksheet by Kuta Software LLC

13) g(x) = 7x + 18

2

15) f (x) = -x + 3

14) f (x) = x + 3 16) f (x) = 4x

Find the inverse of each function. Then graph the function and its inverse.

17) f (x) = -1 - 1 x

5

18) g(x) = 1

x - 1

y 6 5 4 3 2 1

-6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6

1 2 3 4 5 6x

y 6 5 4 3 2 1

-6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6

1 2 3 4 5 6x

19) f (x) = -2x3 + 1

y 6 5 4 3 2 1

-6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6

1 2 3 4 5 6x

20) g(x) = -x - 5

3

y 6 5 4 3 2 1

-6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6

1 2 3 4 5 6x

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Function Inverses

State if the given functions are inverses.

1)

g(x) = 4 -

3 x

2

f (x) = 1 x + 3

2 2

No

3) f (n) = -16 + n

4

g(n) = 4n + 16

Yes

5) f (n) = -(n + 1)3 g(n) = 3 + n3

No

7) f (x) = 4 + 2

-x - 2

h(x) = - 1

x + 3

No

Find the inverse of each function.

9)

h(x) =

3

x

- 3

h-1(x) = (x + 3)3

Name___________________________________ Date________________ Period____

2) g(n) = -12 - 2n

3

f (n) = -5 + 6n

5 No

4) f (x) = - 4 x - 16

7 7

g(x) = 3 x - 3

2 2 No

6) f (n) = 2(n - 2)3

3

g(n) = 4 + 4n

2 Yes

8) g(x) = - 2 - 1

x

f (x) = - 2

x + 1 Yes

10) g(x) = 1 - 2

x

g-1(x) = 1

x + 2

11) h(x) = 2x3 + 3 h-1(x) = 3 x - 3

2

12) g(x) = -4x + 1 g-1(x) = - 1 x + 1

4 4

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Worksheet by Kuta Software LLC

13) g(x) = 7x + 18

2

g-1(x) = 2x - 18

7

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

14) f (x) = x + 3 f -1(x) = x - 3

16) f (x) = 4x f -1(x) = x

4

Find the inverse of each function. Then graph the function and its inverse.

17) f (x) = -1 - 1 x

5

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

y 6 5 4 3 2 1

-6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6

1 2 3 4 5 6x

18) g(x) = 1

x - 1

g-1(x) = 1 + 1

y

x

6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6

1 2 3 4 5 6x

19) f (x) = -2x3 + 1

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

y

2

6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6

1 2 3 4 5 6x

20) g(x) = -x - 5

3

g-1(x) = -3x - 5

y 6 5 4 3 2 1

-6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6

1 2 3 4 5 6x

Create your own worksheets like this one with Infinite Algebra 2. Free trial available at

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Worksheet by Kuta Software LLC

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