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