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In $17-20 :$ a. Find the inverse of each given function. b. Describe the domain and range of each given function and its inverse in terms of the largest possible subset of the real numbers.$$g(x)=x-5$$

a) Therefore the inverse of $\mathrm{g}(\mathrm{x})$ is: $g^{-}(x)=x+5$b) Since $\mathrm{g}(\mathrm{x})$ is linear, its domain and range are both the set of real numbers. This means that the domain and range of its inverse is also the set of real numbers

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 8

Inverse Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

Campbell University

Harvey Mudd College

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Idaho State University

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Hi, everybody. This is section 4.8. Number 18 on the question gives us the function G of X is equal to X minus five. We have to find the inverse of the function on dhe. Also describe the domain and range of both of them. So the first thing that we're going to do is find the inverse in order to find the inverse of a function. What we're doing is switching the X and y value. So I rewrote it. A little simpler G of X equals X minus five. So we have y equals X minus five. I we're going to switch the X and the why and now good X equals Y minus five. And now it's all for the new. I add five to both sides. And why equals X Plus five, which means our G inverse function is equal to X plus five. We have our inverse function and let's talk about the domain and the range for the original function. Our domain is going to bay. Well, really numbers. This is a line. There's no issues with the linear function. So we have the domain is going to be, well, riel numbers Paul rials. I don't realize, and then the range is going to be, well, really. Numbers also. Well, look at the inverse function Y equals MX plus be right. It's still in the form of a lot in a linear function. So again, every linear function will have the domain and range of all riel numbers double reels.

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