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so first I would combine them?
g(f(x)) means you start with g(x), then you replace x with f(x) like this g(x)=-2x^2-3x+5 g(f(x))=-2(f(x))^2-3(f(x))+5 ... replace ALL copies of x with f(x) g(f(x))=-2(3x+2)^2-3(3x+2)+5 ... on the right side, replace ALL copies of f(x) with 3x+2 now expand and simplify
ok so @jim_thompson5910 was @Jhannybean wrong with how she show'd me the other problems?
no I didn't say that
i know but this isn't how she showd me
its possible before you were finding f(x) + g(x) or f(x) - g(x) but now you've moved onto composite functions
so i wanna make sure i did the others correct ly
hopefully you know the difference between them?
they were all composite functions?
oh they were? are you sure?
yup, thats the entire worksheet
alright, then yeah, it was gone about the wrong way
use the method I showed above
uhhh great so would f(x)=-3+2 g(x)=3x^2-x+2 Find (f+g)(x) (f+g)(x)=3x^2-4x is that right? @jim_thompson5910
oh those aren't composite functions
(f+g)(x) = f(x) + g(x)
that's not a composite function
what's the difference?
f(g(x)) or g(f(x)) those are composite functions
but was it still right?
the difference is that with composite functions, you were plugging one entire function into the input of another
f(x)=-3+2 is that right??
there's no x?
there is it's -3x+2
so f(x) = -3x+2 g(x) = 3x^2-x+2 ?
I got 3x^2-4x
(f+g)(x) = f(x) + g(x) (f+g)(x) = -3x+2 + 3x^2-x+2 (f+g)(x) = 3x^2-4x+4
I got 3x^2-4x cuz don't the -2 n +2 cancel eachother out?
the two '2's are positive though
f(x) = -3x+2 g(x) = 3x^2-x+2
ooooo ur right
but you pretty much got it
and this one too? f(x)=x-1 g(x)=2x^2-2x-5 Find g(f(x)) g(f(x))=2x^2-6x-1 is that right?
yep, you got it
well that took long
wait so g(f(x))=-2(3x+2)^2-3(3x+2)+5 would simplify to (-6x+-4)^2-(9x+6)5 @jim_thompson5910
@genius12 it was three problems
not sure how you got (-6x+-4)^2-(9x+6)5
btw you do NOT distribute the -2 through to (3x+2) you have to FOIL out (3x+2)^2 first, then you can distribute
o one sec
not sure how you got (3x+2)^2 to turn into 21x+4
it's magic, it's magic.
I'm a lil confused
what do you get when you FOIL out or expand (3x+2)^2 keep in mind that (3x+2)^2 = (3x+2)(3x+2) (3x+2)^2 = 3x(3x+2) + 2(3x+2) (3x+2)^2 = ???
@jim_thompson5910 my final answer to the problem would be -3(2x+3)(3x+1)
is that correct? lol btw I love how there are like 5 ppl just watching my problem
it's that fascinating lol, but that's if they want you to factor but I'm assuming they just want you to write it in standard form
yeah, I think ur right, in that case it'd be -18x^2-33x-9 i think
g(f(x))=-2(3x+2)^2-3(3x+2)+5 g(f(x)) = -18x^2-33x-9