The function we have is:
[tex]f(x)=4x[/tex]The steps to find the inverse function are:
Step 1. Solve for x.
In this case, we solve for x by dividing both sides of the equation by 4:
[tex]\begin{gathered} \frac{f(x)}{4}=\frac{4x}{4} \\ \frac{f(x)}{4}=x \end{gathered}[/tex]Step 2. Change f(x) for x, and x for the inverse function f^-1(x):
[tex]\frac{x}{4}=f^{-1}(x)\longrightarrow\text{inverse function}[/tex]If we call this inverse function h(x) we get the result:
[tex]h(x)=\frac{x}{4}[/tex]