# Algebra 2/ pre-cal help?

Question:ok guys, i have a summer assignment and need help brushing up on some algebra. i don't necessarily need the answers, just how to do them. (or the answers 0=) )
f(x) = -10x^2-13x-11
g(x) = -15x^3 + 13x^2 - 13x + 13
find f(f(9))

find the domain and range & is it a function?
{ (5,2), (-2,2), (2,2) }
yeah how do i know if it's a function or not?

another thing, how would i factor:
f(x) = 8x^3 - 125
i remember there were rules... i just don't remember how to do it.

thanks =) there are a couple of more.. but i'll just do these first and see how things work out.

1) For the first one, it's called composition of functions. I'm assuming that the problem is f(g(9)). What that means is you put 9 in for x in the g(x) function then take that answer and put it in for x in the f(x) function.

So...
You would do g(9), replace all x's with 9 in the g(x) function.
Then whatever answer you get, that goes in for all of the x's in the f(x) function.

2) The domain is all of the x values. Range is all of the y values.
A function has a distinct characteristic with it's ordered pairs. Each x value has 1 and only 1 y value.
{(1, 2), (1, 3), (2, 4}} is not a function because the x value 1 has two corresponding y values.

Your example has 5, -2, 2 as x values and they all of only y value associated with them. That's a function.

3) Alright, you have f(x) = 8x^3 - 125.

Well, each term is a perfect cube so you can use a special rule for this. This one is a difference of cubes so that special factor rule is...
x^3 - a^3 = (x - a)(x^2 + ax + a^2)

So in this example the first term is 8x^2 and cube root is 2x and the second term has a cube root of 5.

8x^3 - 125 = (2x - 5)(4x^2 + 10x + 25)

As a note, if it was a sum of cubes the form is,
x^3 + a^3 = (x + a)(x^2 - ax + a^2)

I hope that helps.

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