in-17-20-a-find-the-inverse-of-each-given-function-b-describe-the-domain-and-range-of-each-given-f-2

Question

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.
$$
g(x)=x-5
$$

Shira Strong · Accepted Answer

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&#x27;re going to do is find the inverse in order to find the inverse of a function. What we&#x27;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&#x27;re going to switch the X and the why and now good X equals Y minus five. And now it&#x27;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&#x27;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&#x27;s no issues with the linear function. So we have the domain is going to be, well, riel numbers Paul rials. I don&#x27;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&#x27;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.

Aryan Malesha · Answer

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&#x27;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&#x27;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&#x27;s move down here to the inverse. Check out what the domain and ranges here again. X come take on any value. There&#x27;s no there&#x27;s no Value X really can&#x27;t be. And then, as for the range same thing here, why can also take on any value? There&#x27;s no value where, where you can say, like, Oh, there&#x27;s no y value here. Why can basically take on any value out of all the real numbers? So that&#x27;s gonna be all real numbers again

Aryan Malesha · Answer

Okay, So for this problem, we have a function that is f of X equals four X minus three. Now we want to find the inverse of this function. So that&#x27;s which I color the blue. So switch the color blue and you can look at the inverse. So to start off, let&#x27;s just make this f of X. Why just so it&#x27;s a little easier to work with core X minus three and remember, in order to find the inverse, it&#x27;s really simple. We just switch the X and the Y here and then isolate. Why again? So here we&#x27;re gonna have X equals for Why buying this three Now we want to get the while by itself and that will give us the inverse. So to get the wild myself will add three to both sides. So we have X plus three equals for why Then we divide both sides by four to get the why alone? So we have. Why equals X plus 3/4. Now, if we write that out, we can basically say the inverse FX flex is X plus 3/4. So this year is the inverse function. Now the next thing that the problem asks is for the domain and right entry to these. So what connects values be? That&#x27;s the domain looking of y values beef. That&#x27;s the range. So let&#x27;s see, for the domain for this equation, what can the X values here be? Uh, it seems like there&#x27;s no restrictions here, so we know that the dumpling is all real numbers. And as for the range, is there any why value that? Ah, that it can&#x27;t be here. Is there any value where there is no f of X? Is there any value X that you plug in where you don&#x27;t get a result? The answer. There is no. So again here we have all real numbers for the domain and the range. Now, if we go down to the inverse and we try to calculate the same thing over here, we see that the domain looks like all real numbers weaken plug in pretty much any X value. There&#x27;s no X value that, uh, there&#x27;s no X value that doesn&#x27;t work. And then, as for the range, we can also say that this is all real numbers as well. Because again, no matter what x value we play in, there&#x27;s always gonna be a Y value as a result. So there&#x27;s the answer for that course,

Shira Strong · Answer

Hi, everybody. This is section 4.8, number 20. And the question tells us for the function F of X is equal to the square root of X. We have to find the inverse function and then also find the domain and range of the original function and its inverse. So first, let&#x27;s finance first function, we&#x27;re just gonna write it as y equals a squared of X. And then to find the inverse we switch the X and y. So now we&#x27;re going to get X equals the square root of why we wanna square both sides to get rid of the square root. And we get why is equal to X where, which means our inverse function is f inverse of axe is equal to X squared. Now there&#x27;s a little bit of a problem with this. We&#x27;re gonna look in a minute. Let&#x27;s actually look at the graph. First seconds understands it a little bit better. The original function will do that in black. That swearing backs that graph looks like this, right? You can have any negatives under the square root, so it starts at zero, but you can have all the other X values so for to make a little bit of a chart for the domain on the range. Let&#x27;s make a little bit of a chart for F. I tried, OK, after back on and f inverse of X. Okay, here we go. Okay. So for F of X, we could see the domain right from left to right. It starts at zero, and then it&#x27;s gonna go on forever. So it&#x27;s gonna start at zero and then go on forever. So from zero to infinity, the range Well, the lowest to highest. It also starts at zero and is going up for efforts in the range also is from zero to infinity. Now, if we&#x27;re gonna look at the inverse function, the inverse function is a reflection in this line. Why is equal to X y? So if we&#x27;re to graft distal, just do us a little bit better. It&#x27;s a little bit more like that. There you go. Okay, so we&#x27;re gonna look at this graph. X squared is a parabola, right? And the parabola would look like this. The problem is, that whole graph is not reflected from the black one from the original function. Just the right heart is broke. Lunar one after. Let&#x27;s try that. We want to just see the restriction, right? We have the original graph, and then we have the inverse. That will be a reflection over the line. Why will stacks. So the issue is we have to restrict the blue one right, which is our X squared, and we&#x27;re gonna have to restrict it. That it goes from zero to infinity could only start here. We don&#x27;t want the other part of the problem, so the inverse would be f inverse of X equals X squared, where X is greater than or equal to zero. Another way to realize that is well, this domain of the function has to be the range of the inverse because you switch ex ally values and the range of the function must be the domain of the range of the original function. Right? Must be the domain of the inverse. So it happens to all be the same in this case. But because you switched X and Y for the inverse function, you&#x27;ll end up switching the domain on the range

Rae Xin · Answer

so here again were given a function a set of ordered pairs. We need to find the inverse function as well as the domain and range of the inverse function. And we already know that this function is 1 to 1. So basically within determined that each ordered parrot will be reversed, as in the X and the Y values will be flipped. So the inverse function our first ordered pair, it will be negative. Two comma, one falling with negative three comma tube negative 10 kamas, your one common nine and two comma. For now, the rest is also simple where we find our X values her new X values and that will be our domain. And likewise our new Y values will be the new range off the inverse function 1209 and four

Michael Jacobsen · Answer

for this exercise, A 1 to 1 function has been provided here as a set of five different ordered pairs. The first thing we&#x27;re going to do with this 1 to 1 function is note that for any function that&#x27;s oneto one, it will be in vertebral. So it&#x27;s state with the inverse Should be because we&#x27;re given a set of ordered pairs to define our function will define our inverse also as a set of ordered pairs. If we call the first ordered pair from the original function X y that we know to get our first point, we just interchange the role of X and y sold that negative to one here becomes one negative to for the inverse function. Likewise, the second point in the original function is negative 32 But that means to negative three is the second point of the inverse then likewise, the third point is your negative 10. Then we have 91 and the last point on the inverse is for two. So now that we have the inverse, we can determine that domain of this in verse, The domain is a set of all first cornets which are 12 09 and four. So here&#x27;s our domain. It&#x27;ll have the set just the first cornet one, then two, zero, nine and four. Now, to find the range, we do an entirely similar process. The range is the set of all second coordinates, which are negative to negative. Three negative 10 1 and two. So, as a set of elements, the range is negative. Two negative three negative 10 1 and two. So that&#x27;s the domain and range of this inverse function.

Problem

In $17-20 :$ a. Find the inverse of each given fu…

Problem 18 Medium Difficulty

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.
$$
g(x)=x-5
$$

Answer

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

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Anna Marie V.

Kayleah T.

Caleb E.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

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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 2 and Trigonometry

Anna Marie V.

Kayleah T.

Caleb E.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Anna Marie V.

Kayleah T.

Caleb E.

Michael J.

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

Ann Xavier Gantert

Algebra 2 and Trigonometry