Question

What is the inverse of the function f(x) = one-quarterx – 12?

Answer 1

Given:

$\bold{f(x)= \frac{1}{4}x-12}$

To find:

inverse function=?

Solution:

To calculate the inverse function we switch the value in the form of x and y.

So,

$\to f(x)= \frac{1}{4}x-12$ must be written as:

$\to y=\frac{1}{4}x-12$

switch the value in the form of x and y:

$\to x=\frac{1}{4}y-12$

In the above equation we add and subtract the value 12:

$\to x+12= \frac{1}{4}y-12+12\\\\\to x+12= \frac{1}{4}y\\\\\to y= 4x+48$

The inverse function value is: $f^{-1}(x)=4x+48$