anonymous
  • anonymous
Let f(x) = 4x2 + x + 1 and g(x) = x2 – 2. Find g(f(x)). Show each step of your work. Help please
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@marihelenh can you help me with this one too?
anonymous
  • anonymous
@freckles
marihelenh
  • marihelenh
You would replace what you have for f(x) into the x position of g(x). \[\left( 4x ^{2}+x+1 \right)^{2}-2\] Does that make sense?

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anonymous
  • anonymous
but where does the x^2-2 go
anonymous
  • anonymous
the -2 is there but the x^2 i only see the ^2 added but not the x
marihelenh
  • marihelenh
The f(x) becomes a function of g(x), so you just replace what f was equal to into wherever the x is in the g equation.
anonymous
  • anonymous
oh i think i get it
anonymous
  • anonymous
yes i get it :D
marihelenh
  • marihelenh
Ok great! It is a little difficult trying to explain on here sometimes.
anonymous
  • anonymous
4x^4+x^3-1 would this be the final answer?
anonymous
  • anonymous
@marihelenh
marihelenh
  • marihelenh
Just one sec, let me check.
marihelenh
  • marihelenh
No, the answer is actually even longer.
marihelenh
  • marihelenh
To find the answer you would have to do, \[(4x ^{2}+x+1)(4x ^{2}+x+1) -2\]
anonymous
  • anonymous
This is so hard, i thought i understood but now i don't.
marihelenh
  • marihelenh
Do you have to simplify it?
anonymous
  • anonymous
It says Find g(f(x)) so I think I have to but maybe not
marihelenh
  • marihelenh
Well, if you don't have to, you already have your answer, but I will help you simplify it. Just hang in with me. It will seem confusing, but we will get through it and to the answer. OK?
anonymous
  • anonymous
ok, thank you
marihelenh
  • marihelenh
The first thing you should do, is multiply the first term of the first set by the second set. |dw:1436743172709:dw|
anonymous
  • anonymous
16x^5?
marihelenh
  • marihelenh
It would be 16x^4 + 4x^3 + 4x^2
marihelenh
  • marihelenh
Then the same thing with the second term |dw:1436743368652:dw| 4x^3 + x^2 + x
anonymous
  • anonymous
4 times 4 = 16 then 16^4 times x = 16x^5 or the x doesnt add ^1?
marihelenh
  • marihelenh
No, it doesn't. You add the current exponents, so it would be 2 + 2 = 4.
anonymous
  • anonymous
oh ok
marihelenh
  • marihelenh
Then you would do it with the third term. |dw:1436743540161:dw| 4x^2 + x + 1
anonymous
  • anonymous
and what happens to the -2?
marihelenh
  • marihelenh
That will get added on in the end when we put all of the terms together.
anonymous
  • anonymous
so final answer is this 16x^4 + 4x^3 + 4x^2 - 2 ?
marihelenh
  • marihelenh
That is how you multiply the two trinomials out, so then add them all together. \[16x ^{4}+4x ^{3}+4x ^{2}+4x ^{3}+x ^{2}+x+4x ^{2}+x+1-2\] (I added in the -2)
anonymous
  • anonymous
^that last part is so confusing
marihelenh
  • marihelenh
Add like terms \[16x ^{4}+8x ^{3}+9x ^{2}+2x-1\]
marihelenh
  • marihelenh
Do you understand how I got the three different terms on the pictures by multiplying them out?
anonymous
  • anonymous
yes that part i understand
anonymous
  • anonymous
The f(x) becomes a function of g(x) so you just replace what f was equal to into wherever the x is in the g equation. Then you get: (4x^2+x+1)^2(4x^2+x+1)^2-2 then multiply 4x^2 by all terms of second equation to get 16x^4 now multiply x by all terms of second equation to get 4x^3 repeat now with last term to get 4x^2 you get 16x^4 + 4x^3 + 4x^2 now to add the -2 you add like terms to get 16x^4 + 8x^3 + 9x^2 + 2x - 1 would this be good for the answer ?
marihelenh
  • marihelenh
I just put the nine different terms together and then added the -2.
marihelenh
  • marihelenh
Do you just have to explain how to get the answer?
anonymous
  • anonymous
yes
anonymous
  • anonymous
and get the answer too
marihelenh
  • marihelenh
Ok, well then let me just fix what you have, you were pretty close.
anonymous
  • anonymous
ok
marihelenh
  • marihelenh
then multiply 4x^2 by all terms of second equation to get 16x^4+4x^3+4x^2 now multiply x by all terms of second equation to get 4x^3+x^2+x repeat now with last term to get 4x^2+x+1 you get 16x^4+4x^3+4x^2+4x^3+x^2+x+4x^2+x+1 now to add the -2 and add like terms to get 16x^4+8x^3+9x^2+2x-1
marihelenh
  • marihelenh
The first three lines were good. You just had to add a little extra into the next ones, but it was all looking good.
anonymous
  • anonymous
yeah i missed a couple of things, thank you so much for your time :D
marihelenh
  • marihelenh
It's not a problem. I am soooo sorry for how long it took and how confusing it was.
anonymous
  • anonymous
I don't care as long as I get it, thank you.
marihelenh
  • marihelenh
You're welcome

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