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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 f^{-1} (7)

2. If f(3)=2, find f^{-1} (2)

3. If f^{-1} (-4)=-8, find f(-8)

4. If f^{-1} (-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 f^{-1} (0)

d. Solve f^{-1} (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 g^{-1} (1)

d. Solve g^{-1} (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 f^{-1}(0)

d. Solve f^{-1}(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 h^{-1} (5)

d. Solve h^{-1} (t)=1

For each table below, create a table for f^{-1} (x).

11.

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

For each function below, find f^{-1} (x)

13. f(x)=x+3

14. f(x)=x+5

15. f(x)= 2 - x

16. f(x)=3-x

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)=(x-6)^{2}

21. f(x)=x^{2} -5

22. f(x)=x^{2} +1

23. If f(x)=x^{3} -5 and g(x)=\sqrt[{3}]{x+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)=\dfrac{x}{2+x} and g(x)=\dfrac{2x}{1-x}, 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
f^{-1}(x) 3 6 9 13 14

13. f^{-1}(x) = x -3

15. f^{-1}(x) = -x + 2

17. f^{-1}(x) = \dfrac{x - 7}{11}

19. Restricted domain x \ge -7, f^{-1}(x) = \sqrt{x} - 7

21. Restricted domain x \ge 0, f^{-1}(x) = \sqrt{x + 5}

23a. f(g(x)) = (\sqrt[3]{x + 5})^3 - 5 = x
b. g(f(x)) = \sqrt[3]{x^3 - 5 + 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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