Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Verify that $f$ and $g$ are inverse functions using the composition property.$$f(x)=\sqrt{5-x^{2}}, g(x)=\sqrt{5-x^{2}}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Missouri State University

Oregon State University

Baylor University

Lectures

01:02

Verify that $f$ and $g$ ar…

01:32

02:30

00:58

01:40

verify that $f$ and $g$ ar…

02:04

01:12

01:11

00:48

01:14

Use function composition t…

So if they want us to verify, um that these are in verses of each other. Um, since it's the same function, we just need to plug it in one way, and it doesn't matter which way we do it. So it would be either f she composed of X, and this would be the same thing as G composed with Quebec's in this case. So the the square root of five minus f of X squared, which would be the square root of five minus the square root of five ice x squared, squared to the squares. Cancel out. Now we have the square root of five minus five, minus x squared, and then notice how these fives cancel out the negative distributes, and then we would just have the square root of expert. Now, this is where I think they may have forgot to say something, because if we take the square root of this, this is the absolute value of X. And if we come back up here to look at how X is supposed to be, um, for the domain, well, we know that this is going to be greater than or equal to zero on the inside, which would imply five is less than or equal or five is greater than or equal to x squared. And if we take the square root on each side, we get the square root of five less than or equal to X listening to negative route five. So this absolute value here is technically going to be both sides of it. So with just how they're written, these won't be in verses of each other. But I think what they meant to say is that X is greater than equal to zero. And if X is greater than equals zero, then we're just left with X. But without this so technically, uh, technically need X greater than equal to zero for us to actually have this inverse, because again, like I said, otherwise, we don't actually have an inverse at all.

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:43

Write the given expression as a sum of logarithms.$$\log _{2} x y^{2}$$<…

01:31

Solve for $x.$$$4^{x}=23$$

06:13

How long would it take money to double itself if it is earning interest at 1…

Verify that $f$ and $g$ are inverse functions using the composition property…

01:21

Use $\log 2=0.3010$ and $\log 5=0.6990$ and the properties of logarithms to …

03:24

How much should be deposited into an account today if it is to accumulate to…

05:44

(a) Determine the equation of the tangent line at any point $(h, k)$ which l…

07:08

In Exercises $29-38,$ for the function determined by the given equation (a) …

02:51

Find an exponential function determined by the data in Table 6$$\begin{a…