1
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Determine the domain and range of the function f of x is equal to three x squared plus 6 x minus 2.

2
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So the domain of the function is, what is the set of all of the valid inputs, or all of the valid x values for this function.

3
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And I take any real number, square it, multiply it by 3, then add 6 times that real number, and then subtract 2 from it.

4
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So essentially, any number, if we're talking about real, so we're talking about any number, so the domain, the set of valid inputs, the set of inputs over which this function is defined, is all real numbers.

5
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So the domain here is all real numbers. And for those of you who might say, "Well, aren't all numbers real?"

6
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You may or may not know that there is a class of numbers that are a little bit bizarre

7
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when you first learn them, called imaginary numbers and complex numbers

8
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but I wont go into that right now.

9
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But most of the traditional numbers that you know, they are part of the set of real numbers thats pretty

10
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much every thing but complex numbers.

11
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So you take any real number and you put it here, you can square it, multiply it by 3, then add 6 times

12
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it and subtract 2. Now the range at least the way we've been thinking about it in this series of videos ,

13
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the range is the set of possible, outputs of this function or if we said , Y equals F(X)