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Find a formula for the inverse of the function.

$y=x^{2}-x, \quad x \geqslant \frac{1}{2}$

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

Calculus 1 / AB

Chapter 1

Functions and Sequences

Section 5

Logarithms; Semilog and Log-Log Plots

Functions

Oregon State University

University of Michigan - Ann Arbor

Idaho State University

Lectures

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In mathematics, precalculu…

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Finding Inverse Functions …

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03:07

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00:57

um So you want to find down numbers to these equation? Um, So what? You can see dysfunction is something So ladies o XY squared minus x So this function completely than us. Nix my 1/2. It's a word equals one day. I just want for and so that dysfunction is gonna be something like lava Solitary function buddies shifted to to be around 1/2 his shift. 10 down, 1/4. She's gonna be something like these Rothley So that, uh well, it doesn't make any make sense to ask for our neighbors. Onley either. Four points on that side. Four points. That's right. Those are all here. You can only only glee determine what is a numbers rule. So we have this point. Well, you're you on the numbers there is gonna be at that point, we have this point or dangerous there. You see that point? So that is why they would better reception there. So anyway, doing the chambers. So you wantto you want to find why terms of all there's effects, so we'll move the white to the other side of a equation. So over there, where were there? You get a good ready to question before picks square, mindless eggs minus way. So, uh, you want the soul? So for X so Well, these are the circle. Very good question. Um, sold for four. So four bricks That looks like it. Yeah. So, uh, you have sold for X S O. Well, the secretary a question with coefficient. The coach in here a is gonna be one being his mind has one. I see is my nose white? Well, so the general formula were solution of Ecuador. You six. She will go minus B plus or minus. Yes, solutions. Ah, b squared my nose or BC we'll see over to a But in terms of the things that we have there, he's one might as well So my nose, my nose once when that's gonna be one. Laws miners. Well, you know Well, he's square is, uh is wanted. So one minus for a one somewhere on this floor. So we'll see his manners. Why sometimes find his way? His wife, So Oh, So there you have. That is solution. So the stool is one. So what about you? Well, this is gonna be is equal to minus the miners that uses a plus one plus or minus. So whatever you have, Ah, assembly should trouble driving. You must think or what? What solution works? Come on. She worked late observation with plus or the solution with a minus. Like you're the only one to be wants a vision which will be his name. This should have only one solution until you hear that RX needs to be greater than one house. So Well, this is returning it. This is 1/2 plus or minus. That, uh, square it'll run for why or two. So well, if you wanted greater than one, huh? You must speak. Plus, you know, So that is your choice is a plus Sunday. Now, which is the miners, because that is giving you the solution ist line on that side. So the members of dysfunction for ex career people, then one how it's gonna be so that question one, huh? Oh, plus square. Want mine us on, plus for why you too. So that is, uh, 36. I'm, uh well, as you can see here, forget X equals one heart in deploying in there. Why? It goes minus 1/4. So except Miles. What for Is gonna give you what? How which, Uh I hope you can believe it. Go inside to the ground. So for playing in here, where does 1/4 you get X equals 1/2 which is that? Thanks. So the way the st one is here One house there. So that would be the ex, please.

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