Find the inverse of f(x)=(x−10)/(x+10).

Question

Accepted Answer

Welcome back. I'm so glad you're here. We are given this function F of X equals in the numerator. We have eight minus X. And the denominator, we have eight plus X. And we are to find this functions inverse. Alright. The first step in finding the inverse is we're going to rewrite that F of X as a Y equals and then bring down the right hand side eight minus X over eight plus X. And then we're sort of going to enter into the twilight zone a little bit here. We're going to go through this exercise for the purpose of finding the inverse. We're going to swap every Y with an X. So now it's X equals and we're going to swap every X with a Y. So now in the numerator it's eight minus Y over the denominator. Eight plus Y. And now we want to get that Y back by itself on the left hand side where it can be oh, so happy. So we are going to do all of the steps to get Y by itself on the left. So let's start off by multiplying both sides by an eight plus Y. To get rid of that fraction on the right. So the left will now read X times eight plus Y equals on the right, eight minus Y. And now let's distribute this X on the left. And I'm going to write the distributed X up here where we have a bit more room. So now it'll be eight, X plus X, Y equals eight minus Y. And we want to get all the wise onto the left hand side. So let's add Y to both sides. The left hand side will now read eight X plus X. Y plus Y equals eight on the right. And because this eight X. Doesn't have any wise associated with it, let's move that to the right hand side of the equation. The left will just read X, Y plus Y equals and on the right eight minus eight X. Now both of the terms on the left hand side have a. Y. On them. So we can factor A Y in front. So this will be read Y. Parentheses X. Y divided by Y. Is X plus Y divided by Y. Is one equals eight minus eight X on the right now we can divide both sides by X plus one and the right hand side. Well, read eight minus eight X over X plus one in the left hand side. That's just why. Yeah we got Y by itself. But this isn't quite match any of the answer choices. It's very close they have just factored and eight in the numerator. So that will give us one minus X. So eight times one minus X over X plus one. This is our f inverse of X. We look at our answer choices and this matches with answer choice C. Well done. We'll catch you on the next one

Find the inverse of f(x)=(x−10)/(x+10).

Key Concepts

Function Inverses

Rational Functions

Algebraic Manipulation

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