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Finding an Inverse Graphically - Problem 1 3,151 views

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Finding the inverse of a function graphically. So remember in order for a function to have an inverse it has to be one to one. So the first thing we always want to look for is a function one-to-one for every x is there one y for every y is there one x? And then once we pass that what we want to do is flip our graph over the line y equals x.

And so for a little demonstration, what I have here is a little graph. We have our x axis, our y axis and this dotted line is y equals x. This function is one-to-one we can check with the vertical and horizontal line test and what ends up happening is when we flip over the line y equal x everything above the graph gets flipped down and everything below the graph gets flipped up. What you end up with is your new graph of your inverse.

So in general I wouldn’t recommend you making a little picture for every single one but this a little demonstration as to going from the function to an inverse graphically.