WEBVTT
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So in this problem, we're told that F of
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X is equal to X squared plus X and G
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of X is equal to X squared. So we
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want to find the following combinations of these functions along
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with their domains. So start with F plus ci
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. Well, that means to take my ex function
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F function, which is X squared plus X,
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and add it to my GI function, which is
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X squared. Well, I can simplify this by
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combining my light terms. An X squared plus X
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squared is two ex word, so I'm left with
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two x squared plus x. So now for the
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domain well, the domain of both f n g
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are all real numbers because you can plug in any
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value you want and get a value for why?
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And when I combine them, I can also do
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the same thing. So the domain for F plus
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g will be negative. Infinity deposit infinity Now for
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F minus G, that means to take thea function
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, which is X squared plus X and subtracted GI
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function, which is minus X where Well, now
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we want to simplify, so we're gonna combine our
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white terms Well X squared minus X squared zero they
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canceled. So we're just left with Dex. So
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now for the domain. Well, our domains for
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F and G, we're all real numbers in the
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function we get when we subtract them also has a
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domain that's all real numbers. So the domain for
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F minus G is from negative. Infinity deposit infinity
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Now for F times G, That means to take
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my f function X squared plus X and times it
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by my GI function, which is X square.
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So now I can distribute to simplify this which will
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give us X to the fourth plus X to the
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third. Now we can find its domain. Well
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, the domain for both f n g are all
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real numbers and when we multiply him, we get
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a function whose domain is also all real numbers.
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So the domain for F times G is negative.
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Infinity deposit infinity And lastly, we have f divided
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by G. Well, that means to take our
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F function, which is X squared plus x,
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and we're gonna divide it by RG function, which
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is X square. So the only thing we can
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dio is each term in both the numerator and denominator
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can get reduced by an ex. So if I
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do that, I would be love with X plus
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One all over X now for our domain. Well
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, the domain of both f n g is all
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real numbers. However, when we do f divided
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by G know this how and I'm gonna always go
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to my first line. We have the function X
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square in our denominator. We have to make sure
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that X where will not be equal to zero.
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So when is X word equal to zero? Well
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, that happens when X is equal to zero.
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So that means zero cannot be in the domain for
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F divided by G. However, X could be
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anything else. So the domain for F divided by
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G will be negative. Infinity to zero and then
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from zero to infinity.