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Question

Find a formula for the inverse of the function.

$f(x)=\frac{4 x-1}{2 x+3}$

Carlos Pinilla · Accepted Answer

me. Alva is their function. Works people to four ex miners. One works was three. So, uh, I want to find, uh What is it? Members? So you&#x27;re firm enough for what is being very skilled dysfunction so that we will do that. He said he said why? It calls too. That equation that you have there, that function we try to simplify from that equation. What is 26? So here, simplify bye for X. So the way to do that again? Well, the play my dad won so wanted by and by to express three on both sides, he&#x27;s gonna bring it to the side of the question. So you got why them&#x27;s two eggs. Plus really, Is he going to for X might as one? Um, so, uh, a za general. Strange. You do? Well, we can and distribute that. But how? The general is for religious, all these equations, we should, uh, with everything that is in terms of X on one side of the equation, you were trying to solve works and everything that is not in terms of X outside. So, uh, all these one has some terms of X. Some movie there. This dam has not. Some will be to settle a question on A This one is not in terms of our excoriated stays there, on your knees in terms of exile. Let&#x27;s keep it there. So during those two things will move. He&#x27;s won. There is we get out. I was the one. And then when that there is gonna turn negative. So you have another things to move from the left inside, undoing on the right hand side for X that&#x27;s there. And then this guy over there, but minus So why does two Why x so from here, you see that become factor The X It&#x27;s, uh don&#x27;t talk to it, huh? So this expression is equal to x times will there really? For when this is minus two. Why? So you see that? And then with this, we can You can multiply. Well, we can divide like that. More need to that side of the equation. So were modified. They left inside. There are right outside by four minus to Why that he said four there. So I&#x27;ve decided castles. I&#x27;m gonna decide. Well release issue. So from the get no one plus you. Why over But were for blindness. Two. What? No. So there before under X. So before wise getting by these this relation, then find the X In terms of that hope, this is the ex being a the right in terms of our Well, this is Ah, so what I&#x27;m but these insane is that this is Daddy&#x27;s. If ingrates. But it hasn&#x27;t. Well, he&#x27;s a function on white. So these fingers off Why already goes from these equations health you have there. If that takes the sequel to work so you have your plate. If you burst, you&#x27;re playing beavers, too. Sorry. And if you interested that side, we get this equation besides eggs, people toe humors of why, But you want to write it in terms of expo is just the matter over replacing, they&#x27;re why buy eggs on this expression? So if you miss effects is gonna be one plus. So that was a big part of why everyone affects one plus the eggs over for my nose. Through what? So that would be being loose

Amrita Bhasin · Answer

Okay, so sad f of X equal to y and sulfur. Why So if we have y equals four x minus two over three x plus one Rewrite this as three x plus one times y equals four x minus two. This gives us three x y plus y equals four x minus two three x Y minus four. X equals negative to minus. Why four times X equals negative, too. Minus Why so now X equals two. Plus Why over four minus three. Why now? Inverse has to be in terms of X. As you can see, we&#x27;ve got wild here. So simply change the variable X becomes the Empress function of acts. In other words, why and the Y over here becomes acts of two plus x over four Ministry X.

Vishal Parmar · Answer

okay. To find the inverse function we need to interest and a valuable and so far away. So why interchange here we have. It&#x27;s easy quoting or I minus two upon to be right less one. Now here we can multiply X sent through. I bless one of your three ex wife last sex. Is it going to for Roy minus two? Now write all items on the website and all extremes on the right side. You&#x27;re three x Y minus four. White is equal to negative to negative X now here in Victor out white. But your line Marty by three x minus four Is it going toe negative to negative, Rex, No subject right In this aggressions of your wise, it would negative to negative weeks upon three X minus four You hear rising world and express to you ready by four minus three x right, therefore or interest function Ease X plus two upon four Wariness three X Right. Thank you

Rachel Mcbride · Answer

right. So we&#x27;re gonna rewrite this as X equals four F inverse X plus three. So for F inverse, they get X minus three equals four f inverse X divide by four and we get F inverse X equals X minus three all over four. Now we&#x27;re gonna look at three points on the original. So zero with just three half of one with just seven and half of to which is 11. Then we&#x27;re going to compare their points on the inverse look a f in verse three f in verse seven and F in verse 11 f inverse of three is zero seven minus three is four sweet get one and 11 minus three is 88 divided by four is to

Heather Zimmers · Answer

all right, we&#x27;re going to find the inverse of this function, and the first thing I like to do is just call f of X y. So we have y equals four X minus 1/2 X plus three. Now for the inverse we need to interchange or switch X and y So we have X equals before. Why minus 1/2 y plus three. Now we want to isolate Why So let&#x27;s multiply both sides by the denominator. Two y plus three and we have x times a quantity two y plus three equals four y minus one. Now we can distribute the X to get rid of the parentheses, and we have two x y plus three X equals four y minus one. Remember, our goal here is to isolate Why, So we need to get the white terms on one side of the equation and the other terms on the other side. So I&#x27;m going to subtract four wife from both sides, and I have two x y minus four y, and I&#x27;m going to subtract three x from both sides. So this equals negative one minus three x. All right now, it&#x27;s factor. Why out of both terms on the left and we have why Times a quantity two X minus four equals negative one minus three x. Finally, we can divide both sides by two x minus four. So we have y equals negative one minus three x over two X minus four. Now it looks a little bit better with fewer negative signs if we multiply the top by negative one and the bottom by negative one. So that would be one plus three x over four minus two x It&#x27;s equivalent. It just looks a little more slick. And finally, let&#x27;s go ahead and rename this instead of calling it Why, let&#x27;s call it F inverse of X. Make a little more space here F and bursts of X. There we go.

Amrita Bhasin · Answer

this question asked us to find a formula for the inverse of the function. The first step is we need to solve the equation for acts. So given why is one plus square root of two plus three acts, we can get the one over to the left hand side and then we take out the square root. And so we have Y minus one squared is three acts. Therefore, why minus one squared minus two is equivalent to our function, which means that we have axe is 1/3 times y minus one squared minus two, which, substituting for inverse function of acts. We have 1/3 X minus one squared minus two and then we know that acts has to be greater than or equal to one for this to be.

Problem

Find a formula for the inverse of the function. …

Problem 22 Easy Difficulty

Find a formula for the inverse of the function.

$f(x)=\frac{4 x-1}{2 x+3}$

Answer

$f^{-1}(x)=\frac{1+3 x}{4-2 x}$

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James Stewart

Biocalculus Calculus for the Life Sciences

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Precalculus Review - Intro

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$f^{-1}(x)=\frac{1+3 x}{4-2 x}$

Biocalculus Calculus for the Life Sciences

Grace H.

Heather Z.

Kristen K.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Grace H.

Heather Z.

Kristen K.

Joseph L.

James Stewart

Biocalculus Calculus for the Life Sciences