3.7E: Inverse Functions (Exercises)

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Dec 26, 2024
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- 3.7: Inverse Functions
- 4: Linear Functions

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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.

$f(x)=x^{2}+1$
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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