Three-Step Process: Sort the Steps

(1) Solve the equation y = f(x) for x in terms of y

(2) Name the resulting expression in y as f⁻¹(y)

(3) Replace y by x to write the inverse in the form y = f⁻¹(x)

Explanation

Step 1 — Solve for \(x\): rearrange \(y = f(x)\) to get \(x\) explicitly in terms of \(y\). Step 2 — Name it \(f^{-1}(y)\): the expression in \(y\) is the inverse, viewed as a function of \(y\). Step 3 — Replace \(y\) by \(x\): since \(x\) is the conventional independent variable, write \(y = f^{-1}(x)\) so both \(f\) and \(f^{-1}\) use the same axis convention.