WEBVTT
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to find the domain of this function. There are
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a couple of things we want to think about.
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First of all, because we have 1/4 root,
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you have to have something that is non negative inside
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of four through. If you want to get a
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real result, so you need to have either zero
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or positive. And because we have a denominator in
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this problem, we need the denominator to not be
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zero. So actually, we need what's inside the
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fourth route to just be positive. So we need
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X squared minus five x to be greater than zero
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. So how do we solve that inequality? We
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call that a quadratic inequality or a non linear inequality
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. It's a little bit more complicated than solving a
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plane. Linear inequality and the way I would start
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is by factoring X out of both terms. So
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if X Times X minus five is greater than zero
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, so notice that we have a product of two
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things is greater than zero. How can that happen
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? That can happen if you're multiplying, a positive
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and a positive, or if you're multiplying and negative
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and a negative. So we have two cases to
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consider one is if X is greater than zero and
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X minus five is greater than zero. The other
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one is if X is less than zero and X
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minus five is less than zero, So two positives
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multiply to give you a positive two negatives multiply.
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To give you a positive, it has to be
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one or the other. Okay, so let's sell
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both of these. So we have X is greater
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than zero and X is greater than five. OK
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, if you put those two ideas together, the
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only way for both of those to be true at
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the same time is if X is greater than five
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. Now we look at the other two. Inequalities
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X is less than zero and X is less than
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five. The only way for those two things to
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be true at the same time is if X is
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less than zero. So putting all of this together
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exes let X is greater than five or X is
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less than zero, and we can write it like
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this if you want to use interval notation than the
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domain will be negative. Infinity 20 Union five to
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infinity or, if you want to use inequality notation
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, you can say X is less than zero or
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X is greater than five