5.4 Inverse functions
Unit 5 · Rational exponents and radical functions
Ideas in this lesson
Recognize one-to-one functions
An inverse is a function when the original function is one-to-one. A horizontal line must meet its graph at most once.
Find an inverse
Write the rule using y, exchange input and output, and solve for the new output. Exchange the domain and range too.
Verify inverse functions
Both compositions must return the original input throughout their respective domains.
Restrict a domain
Restrict a quadratic to one side of its vertex before taking its inverse. The selected side determines the square-root branch.
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