Question

What is the inverse of the function `f(x) = 1/4x-12`?

Answer 1

`f^(-1)(x)=4x+48`

Explanation:

To find the inverse function, we must switch the roles of `x` and `y` in the equation and solve for `y`

So, we rewrite

`f(x)=1/4x-12`

As...

`y=1/4x-12`

And switch the roles of `x` and `y`

`x=1/4y-12`

And solve for `y`

`xcolor(red)(+12)=1/4ycancel(-12)cancelcolor(red)(+12)`

`x+12=1/4y`

`color(red)4times(x+12)=cancel(color(red)4)times1/cancel4y`

`4x+48=y`

We can now express the inverse function using the notation `f^(-1)(x)`

Thus the inverse function is `f^(-1)(x)=4x+48`