Let y=f(x). To find the inverse of f, isolate x:
[tex]\begin{gathered} f(x)=4x \\ \Rightarrow y=4x \\ \Rightarrow x=\frac{1}{4}y \end{gathered}[/tex]Let x=f^{-1](y). Then:
[tex]f^{-1}(y)=\frac{1}{4}y[/tex]Evaluate the inverse of f at y=x:
[tex]f^{-1}(x)=\frac{1}{4}x[/tex]Therefore, the rule of correspondence of the inverse of f is given by the expression:
[tex]\frac{1}{4}x[/tex]