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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

Practice with function notation:


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


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