Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Find the inverse of each relation. Graph the given relation and its inverse.

8. x	y
   1	0
   2	1
   3	0
   4	2

9. x	y
   1	0
   2	1
   3	2
   4	3

10. x	y
    0	0
    1	1
    2	4
    3	9

11. x	y
    −3	2
    −2	2
    −1	2
    0	2

See Problem 2.

Find the inverse of each function. Is the inverse a function?

12. y = 3 x + 1 y equals 3 x plus 1
13. y = 2 x − 1 y equals 2 x minus 1
14. y = 4 − 3 x y equals 4 minus 3 x
15. y = 5 − 2 x 2 y equals 5 minus , 2 x squared
16. y = x 2 + 4 y equals , x squared , plus 4
17. y = 3 x 2 − 5 y equals , 3 x squared , minus 5
18. y = ( x − 8 ) 2 y equals . open x minus 8 close squared
19. y = ( 3 x − 4 ) 2 y equals . open 3 x minus 4 close squared
20. y = ( 1 − 2 x ) 2 + 5 y equals . open 1 minus 2 x close squared . plus 5

See Problem 3.

Graph each relation and its inverse

21. y = 2 x − 3 y equals 2 x minus 3
22. y = 3 − 7 x y equals 3 minus 7 x
23. y = − x y equals negative x
24. y = 3 x 2 y equals , 3 x squared
25. y = − x 2 y equals negative , x squared
26. y = 4 x 2 − 2 y equals , 4 x squared , minus 2
27. y = ( x − 1 ) 2 y equals . open x minus 1 close squared
28. y = ( 2 − x ) 2 y equals . open 2 minus x close squared
29. y = ( 3 − 2 x ) 2 − 1 y equals . open 3 minus 2 x close squared . minus 1

See Problem 4.

For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function.

30. f ( x ) = 3 x + 4 f open x close equals 3 x plus 4
31. f ( x ) = x − 5 f , open x close , equals , square root of x minus 5 end root
32. f ( x ) = x + 7 f , open x close , equals , square root of x plus 7 end root
33. f ( x ) = − 2 x + 3 f , open x close , equals . square root of negative 2 x plus 3 end root
34. f ( x ) = 2 x 2 + 2 f open x close equals , 2 x squared , plus 2
35. f ( x ) = − x 2 + 1 f open x close equals negative , x squared , plus 1

See Problem 5.

36. Temperature The formula for converting from Celsius to Fahrenheit temperatures is F = 9 5 C + 32 . f equals , 9 fifths c plus 32 .

    1. Find the inverse of the formula. Is the inverse a function?
    2. Use the inverse to find the Celsius temperature that corresponds to 25°F.

37. Geometry The formula for the volume of a sphere is V = 4 3 π r 3 . v equals , 4 thirds , pi , r cubed , .

    1. Find the inverse of the formula. Is the inverse a function?
    2. Use the inverse to find the radius of a sphere that has a volume of 35 , 000  ft  3 . 35 comma 000 , ft cubed . .

See Problem 6.

For Exercises 38-41, f ( x ) = 10 x − 10 . f open x close equals 10 x minus 10 .  Find each value.

38. ( f − 1 ∘ f ) ( 10 ) open , f super negative 1 end super , composition f close open 10 close
39. ( f ∘ f − 1 ) ( − 10 ) open f composition , f super negative 1 end super , close open negative 10 close
40. ( f − 1 ∘ f ) ( 0.2 ) open , f super negative 1 end super , composition f close open 0.2 close
41. ( f ∘ f − 1 ) ( d ) open f composition , f super negative 1 end super , close open d close

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