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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.$$f(x)=\frac{x+5}{3}$$

a) Therefore the inverse of $f(x)$ is: $f^{-}(x)=3 x-5$b) Since $f(x)$ 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

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Okay, So for this problem, we have a function that is f of X equals, um X plus plus five divided by three. And the question basically asks us to find the inverse of dysfunction and then also find the domain and the range of each. So, yeah, let's start by figuring out the inverse. And then we can look at both of the domain and rage. So everything below this blue line will focus on the in burst so we could start by just rewriting this as y equals X plus five over three, just for simplicity sake. Now, the next step here is we want to switch the X and Y in order to figure out what the inverse is. So put the X there. Put the UAE there now, once we solve for why, that will basically give us the inverse. So we want to start by multiplying each side by three. So you get three X equals. Why, plus supplies now to get why alone we subtract five from inside. So we have Why equals three X minus five. So that right there is are inverse expression. Now, if we try to figure out the domain and the range. We know that the domain can really just be all real numbers, because the domain can be all real numbers, because there's no really restrictions X can take on any value. As for the range, the range can also be all real numbers. Because once again we can see that no matter what you plug in for ex and Becks, you can plug in anything. There will always be a Y value, and this is just linear, so it can take on pretty much any y value that there is. Now. Let's move down here to the inverse. Check out what the domain and ranges here again. X come take on any value. There's no there's no Value X really can't be. And then, as for the range same thing here, why can also take on any value? There's no value where, where you can say, like, Oh, there's no y value here. Why can basically take on any value out of all the real numbers? So that's gonna be all real numbers again

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