
# 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.

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 $$f^{-1}(4)$$.