Find inverse functions by solving f(x)=c for simple invertible functions and writing inverse expressions.
Find the inverse of a restricted quadratic by solving for the input
Problem
Find the inverse of \(f(x)=x^2\), \(x\ge~0\).
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What this problem is really about
A quadratic inverse depends on the original domain restriction because solving the swapped equation produces two algebraic branches. We’ll use the allowed inputs to retain one branch, carry the exchanged domain and range into the inverse, and confirm the reversal with both compositions.
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