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Mathematics LibreTexts

3.7E: Inverse Functions (Exercises)

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    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.

    1. \(f(x)=x^{2}+1\)
    2. 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. \(f(x)=-3 x^{2}+x\)
    75. If \(f(5)=2,\) find \(f^{-1}(2)\).
    76. If \(f(1)=4,\) find \(f^{-1}(4)\).