Answer :
To find the inverse fountion interchange the veribles and solve for y.
Answer:
[tex]f^{-1}(x)=4x+48[/tex].
Step-by-step explanation:
We have been given a function [tex]f(x)=\frac{1}{4}x-12[/tex]. We are asked to find the inverse for our given function.
First of all, we will replace [tex]f(x)[/tex] by y as:
[tex]y=\frac{1}{4}x-12[/tex]
Now, we will interchange x and y values as:
[tex]x=\frac{1}{4}y-12[/tex]
Let us solve for y.
[tex]x+12=\frac{1}{4}y-12+12[/tex]
[tex]x+12=\frac{1}{4}y[/tex]
Switch sides:
[tex]\frac{1}{4}y=x+12[/tex]
Multiply both sides by 4:
[tex]4*\frac{1}{4}y=4(x+12)[/tex]
[tex]y=4x+48[/tex]
Therefore, the required inverse function would be [tex]f^{-1}(x)=4x+48[/tex].