3.7E: 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.
- \(f(x)=x^{2}+1\)
-
Given \(f(x)=x^{3}-5\) and \(g(x)=\sqrt[3]{x+5}\) :
- Find \(f(g(x))\) and \(g(f(x))\).
- 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 \(f^{-1}(4)\).