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Prove the inverse function is unique. Hint: assume both $g$ and $h$ are inverse functions of $f$ consider $(g f h)(x)$.

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Campbell University

Harvey Mudd College

Baylor University

Idaho State University

Lectures

02:28

Let $f: \mathrm{X} \righta…

02:29

Proof Prove that if a func…

05:22

Suppose that both $f$ and …

01:16

Inverse Function Property …

So if we want to show that in versus or unique to actually give us a hint of assuming that both G and H R in versus of F and then they wanted us to look at a particular composition being G composed with F composed with h of X. So let's go ahead and go with this here. So first notice. Since F and H are going to be in verses, this is just going to be equal to G of X when we can just say since yes and h are in verses and then we can also right that this is going to be just equal to h of x sense. We're assuming F and G are in verses. But now this implies that h of X is equal to G of X, which would then imply that, um, our inverse so in verse is unique. Since no matter how we do this, we always end up getting that dysfunction. H of X has to be equal to G of X, so they're just the same function. So now that you've finished your proof, you could put your little proof box and smiling face because you're glad you're done with it.

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