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Proving Two Functions are Inverses - Concept 14,697 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!

The definition of a function can be extended to define the definition of an inverse, or an invertible function. It's important to understand proving inverse functions, and the method of proving inverse functions helps students to better understand how to find inverse functions. Students should review how to find an inverse algebraically and the basics of proofs.

Proving two functions are inverses Algebraically. So when we have 2 functions, if we ever want to prove that they're actually inverses of each other, what we do is we take the composition of the two of them. So remember when we plug one function into the other, and we get at x. The key to this is we get at x no matter what the order is. So if we take f of g of x, claiming that f and g are inverses, we should get x. And also if we take g of f of x we should also get x, okay?
There is a chance that this could come out, and one of them could come out to be x, that doesn't prove that we have inverses on our hand. We realy need to do both, if they both come out to be x's. Voila! We have 2 inverses.