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Mathematics LibreTexts

1.6E: Inverse Functions

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section 1.6 exercises

Assume that the function f is a one-to-one function.

1. If f(6)=7, find f1(7)

2. If f(3)=2, find f1(2)

3. If f1(4)=8, find f(8)

4. If f1(2)=1, find f(1)

5. If f(5)=2, find (f(5))1

6. If f(1)=4, find (f(1))1

7. Using the graph of f(x) shown

屏幕快照 2019-06-17 下午5.06.51.png

a. Find f(0)

b. Solve f(x)=0

c. Find f1(0)

d. Solve f1(x)=0

8. Using the graph shown

屏幕快照 2019-06-17 下午5.08.02.png

a. Find g(1)

b. Solve g(x)=1

c. Find g1(1)

d. Solve g1(x)=1

9. Use the table below to find the indicated quantities.

x 0 1 2 3 4 5 6 7 8 9
f(x) 8 0 7 4 2 6 5 3 9 1

a. Find f(1)

b. Solve f(x)=3

c. Find f1(0)

d. Solve f1(x)=7

10. Use the table below to fill in the missing values.

t 0 1 2 3 4 5 6 7 8
h(t) 6 0 1 7 2 3 5 4 9

a. Find h(6)

b. Solve h(t)=0

c. Find h1(5)

d. Solve h1(t)=1

For each table below, create a table for f1(x).

11.

x 3 6 9 13 14
f(x) 1 4 7 12 16

For each function below, find f1(x)

13. f(x)=x+3

14. f(x)=x+5

15. f(x)=2x

16. f(x)=3x

17. f(x)=11x+7

18. f(x)=9+10x

For each function, find a domain on which f is one-to-one and non-decreasing, then find the inverse of f restricted to that domain.

19. f(x)=(x+7)2

20. f(x)=(x6)2

21. f(x)=x25

22. f(x)=x2+1

23. If f(x)=x35 and g(x)=3x+5, find

a. f(g(x))

b. g(f(x))

c. What does this tell us about the relationship between f(x) and g(x)?

24. If f(x)=x2+x and g(x)=2x1x, find

a. f(g(x))

b. g(f(x))

c. What does this tell us about the relationship between f(x) and g(x)?

Answer

1. 6

3. -4

5. 1/2

7a. 3
b. 2
c. 2
d. 2

11.

x 1 4 7 12 16
f1(x) 3 6 9 13 14

13. f1(x)=x3

15. f1(x)=x+2

17. f1(x)=x711

19. Restricted domain x7, f1(x)=x7

21. Restricted domain x0, f1(x)=x+5

23a. f(g(x))=(3x+5)35=x
b. g(f(x))=3x35+5=x
c. This means that they are inverse functions (of each other)


1.6E: Inverse Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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