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

1 Answer
Aug 22, 2017

#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#