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أدلة الدراسة > College Algebra

Solutions

Solutions to Try Its

1. f−1(f(x))=f−1(x+53)=3(x+53)−5=(x−5)+5=x{f}^{-1}\left(f\left(x\right)\right)={f}^{-1}\left(\frac{x+5}{3}\right)=3\left(\frac{x+5}{3}\right)-5=\left(x - 5\right)+5=x and f(f−1(x))=f(3x−5)=(3x−5)+53=3x3=xf\left({f}^{-1}\left(x\right)\right)=f\left(3x - 5\right)=\frac{\left(3x - 5\right)+5}{3}=\frac{3x}{3}=x 2. f−1(x)=x3−4{f}^{-1}\left(x\right)={x}^{3}-4 3. f−1(x)=x−1{f}^{-1}\left(x\right)=\sqrt{x - 1} 4. f−1(x)=x2−32,x≥0{f}^{-1}\left(x\right)=\frac{{x}^{2}-3}{2},x\ge 0 5. f−1(x)=2x+3x−1{f}^{-1}\left(x\right)=\frac{2x+3}{x - 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+4{f}^{-1}\left(x\right)=\sqrt{x}+4 7. f−1(x)=x+3−1{f}^{-1}\left(x\right)=\sqrt{x+3}-1 9. f−1(x)=−x−53{f}^{-1}\left(x\right)=-\sqrt{\frac{x - 5}{3}} 11. f(x)=9−xf\left(x\right)=\sqrt{9-x} 13. f−1(x)=x−53{f}^{-1}\left(x\right)=\sqrt[3]{x - 5} 15. f−1(x)=4−x3{f}^{-1}\left(x\right)=\sqrt[3]{4-x} 17. f−1(x)=x2−12,[0,∞){f}^{-1}\left(x\right)=\frac{{x}^{2}-1}{2},\left[0,\infty \right) 19. f−1(x)=(x−9)2+44,[9,∞){f}^{-1}\left(x\right)=\frac{{\left(x - 9\right)}^{2}+4}{4},\left[9,\infty \right) 21. f−1(x)=(x−92)3{f}^{-1}\left(x\right)={\left(\frac{x - 9}{2}\right)}^{3} 23. f−1(x)=2−8xx{f}^{-1}\left(x\right)={\frac{2 - 8x}{x}} 25. f−1(x)=7x−31−x{f}^{-1}\left(x\right)=\frac{7x - 3}{1-x} 27. f−1(x)=5x−44x+3{f}^{-1}\left(x\right)=\frac{5x - 4}{4x+3} 29. f−1(x)=x+1−1{f}^{-1}\left(x\right)=\sqrt{x+1}-1 31. f−1(x)=x+6+3{f}^{-1}\left(x\right)=\sqrt{x+6}+3 33. f−1(x)=4−x{f}^{-1}\left(x\right)=\sqrt{4-x} Graph of f(x)=4- x^2 and its inverse, f^(-1)(x)= sqrt(4-x). 35. f−1(x)=x+4{f}^{-1}\left(x\right)=\sqrt{x}+4 Graph of f(x)= (x-4)^2 and its inverse, f^(-1)(x)= sqrt(x)+4. 37. f−1(x)=1−x3{f}^{-1}\left(x\right)=\sqrt[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+3{f}^{-1}\left(x\right)=\sqrt{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)=1x{f}^{-1}\left(x\right)=\sqrt{\frac{1}{x}} Graph of f(x)= 1/x^2 and its inverse, f^(-1)(x)= sqrt(1/x). 43. [−2,1)∪[3,∞)\left[-2,1\right)\cup \left[3,\infty \right) Graph of f(x)= sqrt((x+2)(x-3)/(x-1)). 45. [−4,2)∪[5,∞)\left[-4,2\right)\cup \left[5,\infty \right) Graph of f(x)= sqrt((x^2-x-20)/(x-2)). 47. (−2,0);(4,2);(22,3)\left(-2, 0\right); \left(4, 2\right); \left(22, 3\right) Graph of f(x)= x^3-x-2. 49. (−4,0);(0,1);(10,2)\left(-4, 0\right); \left(0, 1\right); \left(10, 2\right) Graph of f(x)= x^3+3x-4. 51. (−3,−1);(1,0);(7,1)\left(-3, -1\right); \left(1, 0\right); \left(7, 1\right) Graph of f(x)= x^4+5x+1. 53. f−1(x)=x+b24−b2{f}^{-1}\left(x\right)=\sqrt{x+\frac{{b}^{2}}{4}}-\frac{b}{2} 55. f−1(x)=x3−ba{f}^{-1}\left(x\right)=\frac{{x}^{3}-b}{a} 57. t(h)=200−h4.9t\left(h\right)=\sqrt{\frac{200-h}{4.9}}, 5.53 seconds 59. r(V)=3V4π3r\left(V\right)=\sqrt[3]{\frac{3V}{4\pi }}, 3.63 feet 61. n(C)=100C−25.6−Cn\left(C\right)=\frac{100C - 25}{.6-C}, 250 mL 63. r(V)=V6πr\left(V\right)=\sqrt{\frac{V}{6\pi }}, 3.99 meters 65. r(V)=V4πr\left(V\right)=\sqrt{\frac{V}{4\pi }}, 1.99 inches

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