How do you find the inverse of ##f(x) = 3x – 6 ## and is it a function?

The inverse is ##y=1/3x+2##, a line with a slope of ##1/3## and a ##y## intercept of ##2##. Clearly this would pass the vertical line test, making it a function.

It is easier to deal with the symbols if you begin to find the inverse of ##f(x) = 3x-6## by replacing ##f(x)## with ##y##.

##y=3x-6## We know switch the ##x## and the ##y##.

##x=3y-6##

This equation is now the inverse written in implicit form, an idea that will come back in Calculus. We say that it is in implicit form because it is not solved for ##y##. We now solve for ##y## to get it in explicit form.

##x+6=3y##

##(x+6)/3=y##

##y=1/3x+2##

We recognize this from Algebra class as a line with a slope of ##1/3## and a##y## intercept of ##2##. Clearly this would pass the vertical line test, making it a function.