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Domain and range of a function given a formula | Algebra II | Khan Academy

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Determine the domain and range

of the function f of x is equal to 3x squared plus 6x minus 2.

So, the domain of the function is: what is a set of all of the valid inputs,

or all of the valid x values for this function?

And, I can take any real number, square it, multiply it by 3,

then add 6 times that real number and then subtract 2 from it.

So essentially any number if we're talking about reals when we talk 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.

So, the domain here is all real numbers.

And, for those of you who might say, well, you know, aren't all numbers real?

You may or may not know that there is a class of numbers,

that are a little bit bizarre when you first learn them,

called imaginary numbers and complex numbers.

But, I won't go into that right now.

But, most of the traditional numbers that you know of,

they are part of the set of real numbers.

It's pretty much everything but complex numbers.

So, you take any real number and you put it here,

you can square it, multiply it by 3, then add 6 times it and subtract 2.

Now, the range, at least the way we've been thinking about it