3.7 Inverse functions  (Page 6/9)

Try It

Draw graphs of the functions $f$ and $f^{-1}$ from [link] .

Got questions? Get instant answers now!

Visit this website for additional practice questions from Learningpod.

Key concepts

• If $g(x)$ is the inverse of $f(x),$ then $g(f(x))=f(g(x))=x.$ See [link] , [link] , and [link] .
• Only some of the toolkit functions have an inverse. See [link] .
• For a function to have an inverse, it must be one-to-one (pass the horizontal line test).
• A function that is not one-to-one over its entire domain may be one-to-one on part of its domain.
• For a tabular function, exchange the input and output rows to obtain the inverse. See [link] .
• The inverse of a function can be determined at specific points on its graph. See [link] .
• To find the inverse of a formula, solve the equation $y=f(x)$ for $x$ as a function of $y.$ Then exchange the labels $x$ and $y.$ See [link] , [link] , and [link] .
• The graph of an inverse function is the reflection of the graph of the original function across the line $y=x.$ See [link] .

Section exercises

Verbal

Algebraic

For the following exercises, find $f^{-1}(x)$ for each function.

For the following exercises, find a domain on which each 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.