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Alright, what I want to do is show you how to determine when your value of x when f of x equals g of x.
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So what we're going to do is we're going to find the value of x when these two functions are equal to each other.
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So what they said in the problem is we want to determine what happens when we have f of x equals g of x.
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So before we've looked at when we find the value of x when f of x equals zero.
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So what we did was we put a zero in for the f of x and then just self-rex.
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Well now we're given this constraint where we want f of x to equal g of x.
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So we know f of x is the square root of 3x plus 1 and g of x is x plus 1.
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So if we want them equal each other we're just going to write square root of 3x plus 1 equals x plus 1.
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So that's pretty much all we do. We say f of x equal g of x.
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We know what f of x and g of x are that's given to us.
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So we set them equal to each other.
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Now the fun part is we have to go and do our algebra to solve for x.
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So the first thing we need to do is we need to learn how to get these x's on to the same side.
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Or at least we need to find a way to combine them.
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The first thing I'm going to do is I'm just going to subtract the 1.
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I know these both have positive 1.
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So if I subtract the 1 on both sides, if I subtract the 1 over here that's going to cast the law.
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So therefore I'm going to cast the law.
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So I left with a 3x equals x.
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Or the square root, I'm sorry, 3x equals x.
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So again, before I go and get this x over to the same side,
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though, I'm going to want to get rid of the square root.
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So that's exactly what I'm going to do.
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To get rid of the square root, I can square both sides.
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And so that's going to go ahead and cancel out.
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So therefore I'm left with 3x equals x squared.
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Now I'm going to want to get these over to the same side.
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And then remember whenever we're dealing with the power of R1,
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we want to start looking into if we can get our x's as a set of linear factors.
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Because once we get to linear factors, we'll be able to factor it in the solve form.
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So I'm going to subtract 3x.
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And I'm actually just going to continue the problem here.
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So I have 0 equals x squared minus 3x.
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So now what I can do is I can look at this and I say, all right, well,
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I still don't know what x is, right?
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I need some way to go and factor it out.
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So I notice that they both share an x.
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So what I'm going to do is factor out, back an x.
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So therefore I have 0 equals factor up x.
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And we have x minus 3.
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And the important thing, what happened, the reason why you always want to look to this is
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because now I have a set of linear factors, where x times x minus 3,
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and either one of these can make that equal to 0.
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So your two possible answers for x could be, you could either say,
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x could equal 0, or you could say if x was equal to 3,
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or actually, let me show you why x equals 3.
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Or you could say, 0 equals x minus 3.
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So now when I add three on the both sides,
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I get my two solutions, are x equals 0 and x equals 3.
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And pretty much what we're showing you is, you know,
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you plugged into 3 in there, 3 minus 3 would be 0.
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0 times, you know, 3 would be 0 again.
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Or if you plugged into 0 and 4x, 0 times negative 3 would be 0 again.
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So therefore your two solutions, when f of x equals g of x,
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is 0 and 3.
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Next up,