3.9E: Inverse Functions (Exercises)

For the following exercises, find \(f^{-1}(x)\) for each function.

69. \(f(x)=9+10 x\)
70. \(f(x)=\frac{x}{x+2}\)

For the following exercise, find a domain on which the function \(f\) is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of \(f\) restricted to that domain.

71. \(f(x)=x^{2}+1\)
72. Given \(f(x)=x^{3}-5\) and \(g(x)=\sqrt[3]{x+5}\) :
    1. Find \(f(g(x))\) and \(g(f(x))\).
    2. What does the answer tell us about the relationship between \(f(x)\) and \(g(x)\) ?

For the following exercises, use a graphing utility to determine whether each function is one-to-one.

73. \(f(x)=\frac{1}{x}\)
74. \(f(x)=-3 x^{2}+x\)

Practice with function notation:

75. If \(f(5)=2,\) find \(f^{-1}(2)\).
76. If \(f(1)=4,\) find \(f^{-1}(4)\).