Problem

If the function is one-to-one, find its inverse. …

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Problem 16 Medium Difficulty

If the function is one-to-one, find its inverse.
$g(x)=\sqrt{x+2}, \quad x \geq-2$

Answer

$f^{-1}(x)=x^{2}-2, x \geq 0$

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Algebra

Beginning and Intermediate Algebra

Chapter 12

Inverse, Exponential, and Logarithmic Functions

Section 1

Inverse Functions

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Video Transcript

So here we have the function G of X is equal to discriminate of X plus two without restricted the main. That X can only be greater than or equal to native to to the way that we're going to show that this is a 1 to 1 function. It's by graphically. Okay, that time you try to show you. So we're gonna graph it and we're gonna use the table. So excuse going to be greater than or equal to negative twos. We're gonna do negative too, *** One. And to so every plug in a negative two for X, we get negative two plus two, which is Cyril and squinted of zero is zero. And then we have negative one plus do, which is a positive one was acquitted of one. It's just one. And then we have two plus two, which is four and a squadron of war is to So now we're going to graph it. We have a negative two and syrah negative one and one, and then we have two and two. So this is kind of whether function is gonna look like. And so if we do the horizontal line test, we see that it posits it because it only touches it one. So this is 1 to 1. So now we're going to find its members. So we're going to write it as why is equal to the square root of X plus two. And so we're going to switch the X and the boy. We're gonna have excess equal to the square root of white close to, and we're gonna sell For what? So first, to get rid of that the square root we're gonna square Could we get X squared is equal to y plus two. Then we're gonna get little to vice to trap him. So we get X squared minus two is equal to why. And so we're gonna write this as the embers function is then equal to X squared minus two. Now we look up here, we see that we had a restricted remains and we need to restrict the main of this one. And we're going to say that X can only be greater than or equal to syrup because this X square is a parabola. And so we're only gonna be used in the, um, the positive numbers. And so that is going to be our answer. Okay,

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