Function Composition & Inverses - Mrs. Rivero's Math Classes

[Pages:3]Algebra 2

Function Composition & Inverses

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Find the inverse of each function.

1)

g(x) = -4 +

1 x

5

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2)

g(n) = -3 -

1 n

2

3) f (n) = -2n5 + 3

4)

g(n) =

3

n-3 -1

5) h(n) = 2 + 3

n

State if the given functions are inverses.

6) f (x) = 1 x + 1

2 2

g(x) = 2x - 1

7) g(x) = x - 1 f (x) = 2 + 3 x

5

8)

g(n) =

3

-n - 1

f (n) = (n - 3)3

9)

g(x) =

3

x

f (x) =

5

x + 1

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Worksheet by Kuta Software LLC

10) f (x) = 2 + 1

x + 2

h(x) = - 2 - 2

-x + 1

Perform the indicated operation.

12) g(t) = 4t - 2 h(t) = t + 4 Find g(h(t))

14) g(n) = n + 4 h(n) = 3n + 4 Find g(h(n))

16) f (t) = -2t2 + 4 g(t) = t - 5 Find f (g(t))

18) f (x) = x + 2 g(x) = 3x - 4 Find f (g(x))

20) f (a) = -3a3 - 2 g(a) = a + 4 Find f (g(a))

11) h(x) = 4

-x + 2

f (x) = - 3

x - 1

13) g(x) = 4x + 3 f (x) = x2 - 4 Find g( f (x))

15) f (x) = x3 - 2x g(x) = 3x Find f (g(x))

17) h(t) = -3t + 4 g(t) = t2 + 4t Find h(g(t))

19) h(x) = 4x + 3 Find h(h(x))

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Worksheet by Kuta Software LLC

Answers to Function Composition & Inverses

1) g-1(x) = 5x + 20

2) g-1(n) = -2n - 6

5) h-1(n) = 2

n - 3

6) Yes

9) No

10) Yes

13) 4x2 - 13

14) 3n + 8

17) -3t2 - 12t + 4

18) 3x - 2

20) -3a3 - 36a2 - 144a - 194

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

2 7) No

11) No 15) 27x3 - 6x 19) 16x + 15

4) g-1(n) = 3 + (n + 1)3

8) No

12) 4t + 14 16) -2t2 + 20t - 46

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Worksheet by Kuta Software LLC

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