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# 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.