anonymous
  • anonymous
PLEASE HELP!!! Let f(x) = 3x^2 – x + 2 and g(x) = 5x2 – 1. Find f(g(x)).
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
anonymous
  • anonymous
is it 5x^2-1 or 5x=2-1?
anonymous
  • anonymous
5x+2-1

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anonymous
  • anonymous
sorry it's g(x) = 5x^2 - 1
anonymous
  • anonymous
oh okay
anonymous
  • anonymous
are you looking for where they intersect
anonymous
  • anonymous
?
anonymous
  • anonymous
no I'm looking for f(g(x))
anonymous
  • anonymous
whats F(g(x))?
anonymous
  • anonymous
I'm not sure, which is why I need help
anonymous
  • anonymous
oh
Jhannybean
  • Jhannybean
take your function, \(f(\color{red}{x}) = 3\color{red}{x^2}-\color{red}{x}+2\) and replace every red colored x with \(\color{red}{5x^2-1}\)
Jhannybean
  • Jhannybean
Simplify that and you will have \(f(g(x))\)
anonymous
  • anonymous
okay, let me work this out
Jhannybean
  • Jhannybean
There was a typo, haha. \[f(g(x)) = 3(5x^2-1)^2 -(5x^2-1) +2\]
anonymous
  • anonymous
Refer to the attachment from the Mathematica program.
1 Attachment
anonymous
  • anonymous
okay, I think I worked it out. is the answer f(g(x)) = 25x^4 - 6 ?!?!
Jhannybean
  • Jhannybean
\[f(g(x)) = 3( 24x^4-10x^2+1) -5x^2+1+2\]\[f(g(x)) = 72x^4 -30x^2+3-5x^2+3\]\[f(g(x))= 72x^4-(30+5)x^2+6\]\[\boxed{\color{red}{f(g(x)) = 72x^4 -35x^2+6}}\]
Jhannybean
  • Jhannybean
I think you made a mistake expanding \((5x^2-1)^2\)
anonymous
  • anonymous
wait, how did you get from f(g(x))=3(5x^2−1)^2−(5x^2−1)+2 to f(g(x))=3(24x^4−10x^2+1)−5x^2+1+2
anonymous
  • anonymous
Jhannybean
  • Jhannybean
I expanded \((5x^2-1)^2\) Think of \(a=5x^2\) and \(b=1\). Now do you recall the form \(ax^2-2ab+b^2\)? This is the expansion of a polynomial in the form \((a-b)^2\)
Jhannybean
  • Jhannybean
Are you with me so far?
anonymous
  • anonymous
oh. but then shouldn't it be f(g(x)) = 75x^4 - 30x^2 + 3 − 5x^2 + 1 + 2 instead of having 72x^4?
anonymous
  • anonymous
f(g(x)) = 3(5x^2 - 1)^2 - (5x^2 - 1) + 2 f(g(x)) = 3(25x^4 - 10x^2 + 1) - (5x^2 - 1) + 2 f(g(x)) = 75x^4 - 30x^2 + 3 - 5x^2 + 1 + 2 f(g(x)) = 72x^4 - 35x^2 + 6
Jhannybean
  • Jhannybean
Oh yes it was my fault. I found it. I wrote 24 instead of 25. You are right. It should be 75 ^^
Jhannybean
  • Jhannybean
\[f(g(x)) = 3( \color{blue}{24x^4}-10x^2+1) -5x^2+1+2\] SO when I was solving it I got 72x\(^4\) instead of 75x\(^4\)
anonymous
  • anonymous
oh, so the answer is f(g(x)) = 75x^4 - 35x^2 + 6?
Jhannybean
  • Jhannybean
Yep.
anonymous
  • anonymous
thanks :)
Jhannybean
  • Jhannybean
Good job on spotting that error.
anonymous
  • anonymous
lol thanks

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