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Proving Two Functions are Inverses  Concept
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel 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.
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Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
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Proving Two Functions are Inverses
Problem 1 6,544 viewsProve f(x) = 6x − 3 and g(x) = ⅙(x + 3) are inverses.

Proving Two Functions are Inverses
Problem 2 4,005 viewsProve f(x) = 2(x + 3) and f⁻¹(x) = ½x + 3 are inverses.

Proving Two Functions are Inverses
Problem 3 910 views 
Proving Two Functions are Inverses
Problem 4 945 views
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