anonymous
  • anonymous
f(x)=3x+2 g(x)=-2x^2-3x+5 Find g(f(x)) @Jhannybean
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
so first I would combine them?
anonymous
  • anonymous
so 3x+2-2x^2-3x+5=g(f(x))
anonymous
  • anonymous
g(f(x))=-2x^2+7 right?@Jhannybean

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jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
ok so @jim_thompson5910 was @Jhannybean wrong with how she show'd me the other problems?
jim_thompson5910
  • jim_thompson5910
no I didn't say that
anonymous
  • anonymous
i know but this isn't how she showd me
jim_thompson5910
  • jim_thompson5910
its possible before you were finding f(x) + g(x) or f(x) - g(x) but now you've moved onto composite functions
anonymous
  • anonymous
so i wanna make sure i did the others correct ly
jim_thompson5910
  • jim_thompson5910
hopefully you know the difference between them?
anonymous
  • anonymous
they were all composite functions?
jim_thompson5910
  • jim_thompson5910
oh they were? are you sure?
anonymous
  • anonymous
yup, thats the entire worksheet
jim_thompson5910
  • jim_thompson5910
alright, then yeah, it was gone about the wrong way
jim_thompson5910
  • jim_thompson5910
use the method I showed above
anonymous
  • anonymous
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
jim_thompson5910
  • jim_thompson5910
oh those aren't composite functions
jim_thompson5910
  • jim_thompson5910
(f+g)(x) = f(x) + g(x)
jim_thompson5910
  • jim_thompson5910
that's not a composite function
anonymous
  • anonymous
what's the difference?
jim_thompson5910
  • jim_thompson5910
f(g(x)) or g(f(x)) those are composite functions
anonymous
  • anonymous
ooooooooooo
anonymous
  • anonymous
but was it still right?
jim_thompson5910
  • jim_thompson5910
the difference is that with composite functions, you were plugging one entire function into the input of another
jim_thompson5910
  • jim_thompson5910
f(x)=-3+2 is that right??
anonymous
  • anonymous
yup
jim_thompson5910
  • jim_thompson5910
there's no x?
anonymous
  • anonymous
there is it's -3x+2
anonymous
  • anonymous
my bad
jim_thompson5910
  • jim_thompson5910
so f(x) = -3x+2 g(x) = 3x^2-x+2 ?
anonymous
  • anonymous
yup
anonymous
  • anonymous
find (f+g)(x)
anonymous
  • anonymous
I got 3x^2-4x
jim_thompson5910
  • jim_thompson5910
(f+g)(x) = f(x) + g(x) (f+g)(x) = -3x+2 + 3x^2-x+2 (f+g)(x) = 3x^2-4x+4
anonymous
  • anonymous
u sure?
anonymous
  • anonymous
I got 3x^2-4x cuz don't the -2 n +2 cancel eachother out?
jim_thompson5910
  • jim_thompson5910
the two '2's are positive though
jim_thompson5910
  • jim_thompson5910
f(x) = -3x+2 g(x) = 3x^2-x+2
anonymous
  • anonymous
ooooo ur right
jim_thompson5910
  • jim_thompson5910
silly mistake
jim_thompson5910
  • jim_thompson5910
but you pretty much got it
anonymous
  • anonymous
haha :)
anonymous
  • anonymous
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?
jim_thompson5910
  • jim_thompson5910
yep, you got it
anonymous
  • anonymous
u rock!!!!!!!!!!!!!!!!!!!!!!!
jim_thompson5910
  • jim_thompson5910
thx lol
anonymous
  • anonymous
well that took long
anonymous
  • anonymous
wait so g(f(x))=-2(3x+2)^2-3(3x+2)+5 would simplify to (-6x+-4)^2-(9x+6)5 @jim_thompson5910
anonymous
  • anonymous
@genius12 it was three problems
anonymous
  • anonymous
ok lol
jim_thompson5910
  • jim_thompson5910
not sure how you got (-6x+-4)^2-(9x+6)5
anonymous
  • anonymous
multiply
jim_thompson5910
  • jim_thompson5910
btw you do NOT distribute the -2 through to (3x+2) you have to FOIL out (3x+2)^2 first, then you can distribute
anonymous
  • anonymous
o one sec
anonymous
  • anonymous
(21x+4)
jim_thompson5910
  • jim_thompson5910
not sure how you got (3x+2)^2 to turn into 21x+4
anonymous
  • anonymous
-18x^2-33x-9
anonymous
  • anonymous
it's magic, it's magic.
anonymous
  • anonymous
I'm a lil confused
jim_thompson5910
  • jim_thompson5910
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 = ???
anonymous
  • anonymous
@jim_thompson5910 my final answer to the problem would be -3(2x+3)(3x+1)
anonymous
  • anonymous
is that correct? lol btw I love how there are like 5 ppl just watching my problem
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
yeah, I think ur right, in that case it'd be -18x^2-33x-9 i think
jim_thompson5910
  • jim_thompson5910
correct
anonymous
  • anonymous
coolio ty!!!!!!!!!!!!!!!!!!!!
jim_thompson5910
  • jim_thompson5910
g(f(x))=-2(3x+2)^2-3(3x+2)+5 g(f(x)) = -18x^2-33x-9
jim_thompson5910
  • jim_thompson5910
yw

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