Answer :

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]

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