Answer:
[tex]\huge\boxed{f^{-1}(x)=4x+48}[/tex]
Step-by-step explanation:
In order to find the inverse of a function, we need to follow a couple of steps.
We can follow these steps to find the inverse of this function.
Step 1: We can just replace the f(x) with y, making our function [tex]y=\frac{1}{4}x-12[/tex].
Step 2: We can swap where the x and y values are, making our equation
[tex]x = \frac{1}{4}y-12[/tex]
Step 3: We can now solve for y.
We now have the function as [tex]y = 4x+48[/tex].
Step 4: We can now replace the y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x) =4x+48[/tex]
Therefore the inverse of [tex]f(x) = \frac{1}{4}x-12[/tex] is [tex]f^{-1}(x) =4x+48[/tex].
Hope this helped!
