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.
Answers:
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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