Solutions

Solutions to Try Its

1. f−1(f(x))=f−1(x+53)=3(x+53)−5=(x−5)+5=xf−1(f(x))=f−1(x+53)=3(x+53)−5=(x−5)+5=x and f(f−1(x))=f(3x−5)=(3x−5)+53=3x3=xf(f−1(x))=f(3x−5)=(3x−5)+53=3x3=x

2. f−1(x)=x3−4f−1(x)=x3−4

3. f−1(x)=√x−1f−1(x)=√x−1

4. f−1(x)=x2−32,x≥0f−1(x)=x2−32,x≥0

5. f−1(x)=2x+3x−1f−1(x)=2x+3x−1

Solutions to Odd-Numbered Exercises

1. It can be too difficult or impossible to solve for x in terms of y.

3. We will need a restriction on the domain of the answer.

5. f−1(x)=√x+4f−1(x)=√x+4

7. f−1(x)=√x+3−1f−1(x)=√x+3−1

9. f−1(x)=−√x−53f−1(x)=−√x−53

11. f(x)=√9−xf(x)=√9−x

13. f−1(x)=3√x−5f−1(x)=3√x−5

15. f−1(x)=3√4−xf−1(x)=3√4−x

17. f−1(x)=x2−12,[0,∞)f−1(x)=x2−12,[0,∞)

19. f−1(x)=(x−9)2+44,[9,∞)f−1(x)=(x−9)2+44,[9,∞)

21. f−1(x)=(x−92)3f−1(x)=(x−92)3

23. f−1(x)=2−8xxf−1(x)=2−8xx

25. f−1(x)=7x−31−xf−1(x)=7x−31−x

27. f−1(x)=5x−44x+3f−1(x)=5x−44x+3

29. f−1(x)=√x+1−1f−1(x)=√x+1−1

31. f−1(x)=√x+6+3f−1(x)=√x+6+3

33. f−1(x)=√4−xf−1(x)=√4−x
Graph of f(x)=4- x^2 and its inverse, f^(-1)(x)= sqrt(4-x).

35. f−1(x)=√x+4f−1(x)=√x+4
Graph of f(x)= (x-4)^2 and its inverse, f^(-1)(x)= sqrt(x)+4.

37. f−1(x)=3√1−xf−1(x)=3√1−x
Graph of f(x)= 1-x^3 and its inverse, f^(-1)(x)= (1-x)^(1/3).

39. f−1(x)=√x+8+3f−1(x)=√x+8+3
Graph of f(x)= x^2-6x+1 and its inverse, f^(-1)(x)= sqrt(x+8)+3.

41. f−1(x)=√1xf−1(x)=√1x
Graph of f(x)= 1/x^2 and its inverse, f^(-1)(x)= sqrt(1/x).

43. [−2,1)∪[3,∞)[−2,1)∪[3,∞)
Graph of f(x)= sqrt((x+2)(x-3)/(x-1)).

45. [−4,2)∪[5,∞)[−4,2)∪[5,∞)
Graph of f(x)= sqrt((x^2-x-20)/(x-2)).

47. (−2,0);(4,2);(22,3)(−2,0);(4,2);(22,3)
Graph of f(x)= x^3-x-2.

49. (−4,0);(0,1);(10,2)(−4,0);(0,1);(10,2)
Graph of f(x)= x^3+3x-4.

51. (−3,−1);(1,0);(7,1)(−3,−1);(1,0);(7,1)
Graph of f(x)= x^4+5x+1.

53. f−1(x)=√x+b24−b2f−1(x)=√x+b24−b2

55. f−1(x)=x3−baf−1(x)=x3−ba

57. t(h)=√200−h4.9t(h)=√200−h4.9, 5.53 seconds

59. r(V)=3√3V4πr(V)=3√3V4π, 3.63 feet

61. n(C)=100C−25.6−Cn(C)=100C−25.6−C, 250 mL

63. r(V)=√V6πr(V)=√V6π, 3.99 meters

65. r(V)=√V4πr(V)=√V4π, 1.99 inches