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.$$f(x)=2 x-3, g(x)=\frac{x+3}{2}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:14

Verify that $f$ and $g$ ar…

02:04

01:04

Use composition of functio…

00:58

03:05

verify that $f$ and $g$ ar…

00:46

01:32

Use function composition t…

01:02

Verify that the given func…

02:55

01:06

So if we want to verify that these are in versus by composition, what we need to do is first start by doing F composed with G of X, and then we want to see if this is just equal to X, and then we're going to do the same thing in the opposite order. So this would be two times G f X minus three. And so that would be, um, two times X plus 3/2 minus three. So the tombs cancel out. They were left with X plus three minus three. The threes cancel, and then we're just left with X. So this first way checks out. Now we need to do it in the opposite order. So we do g of Alfa Becks, and this is going to be, uh, f of X plus 3/2. Then we plug in f of x two x minus three plus 3/2. So the threes cancel when we get to X over two, the two's cancel and then we're just sucked with X, which also gives us X. So you can see we can compose these in either order and we are just left to effects, so therefore they should be in verses of each other

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:59

Use the properties of logarithms to find the derivative. Hint: It might be e…

01:25

Combine the given expression into a single logarithm.$$2 \log _{3} 4-\lo…

01:30

Solve for $x.$$$\frac{2^{x}-16 \cdot 2^{-x}}{2}=3$$

01:17

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

02:35

Use logarithmic differentiation to find the derivative.$$y=\left(x^{2}+5…

00:40

Determine $f^{\prime}(x)$.$$f(x)=\ln a x, a>0$$

06:28

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

01:45

Write the given expression as a sum of logarithms.$$\ln \frac{x^{3} y^{4…

01:58

Given the functions you found in Example $59,$ suppose you are later given a…

03:55

A producer finds that demand for his commodity obeys a linear demand equatio…