anonymous
  • anonymous
Let f(x) = 4x2 + x + 1 and g(x) = x2 – 2. Find g(f(x)). Show each step of your work. Please don't just give the answer! Walk me through it. Thank you!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Vocaloid
  • Vocaloid
g(f(x)) means take f(x) and substitute it for x in g(x)
Vocaloid
  • Vocaloid
g(x) = x^2 - 2 g(f(x)) = f(x)^2 - 2 = (4x^2 + x + 1)^2 - 2 finish by expanding
jdoe0001
  • jdoe0001
actaully it was the other way around... anyhow =)

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More answers

anonymous
  • anonymous
i'm confused now. what do you mean the other way around?
jdoe0001
  • jdoe0001
\(\bf f(x) ={\color{brown}{ 4x^2+x+1}}\qquad g(x)={\color{black}{ x^2-2}} \\ \quad \\ g(\ {\color{brown}{ f(x)}}\ )=({\color{brown}{ f(x)}})^2-2\)
jdoe0001
  • jdoe0001
expand as Vocaloid suggested
anonymous
  • anonymous
okay... so g(f(x)) = (4x^2 + x + 1)^2 - 2. I'm probably way off, but 16x^4 + x^2 + 2 - 2.
jdoe0001
  • jdoe0001
just bear in mind that \(\bf (4x^2 + x + 1)^2 \implies (4x^2 + x + 1)(4x^2 + x + 1)\)
anonymous
  • anonymous
so was I right? I just had to take away the -2 at the end?
anonymous
  • anonymous
What are the steps I have to take? Maybe I can figure it out if you tell me the steps to get the answer. Thanks so much for helping me by the way.
Vocaloid
  • Vocaloid
not quite (4x^2 + x + 1)^2 = (4x^2 + x + 1)*(4x^2 + x + 1) use foil to expand
anonymous
  • anonymous
Okay. Foil = First, outer, inner, last?
Vocaloid
  • Vocaloid
yes
Vocaloid
  • Vocaloid
we also have a middle term in this case, x
anonymous
  • anonymous
a sec. pls
anonymous
  • anonymous
so it would be x squared in the middle
Vocaloid
  • Vocaloid
|dw:1443485986922:dw|
Vocaloid
  • Vocaloid
|dw:1443486003860:dw|
Vocaloid
  • Vocaloid
|dw:1443486036186:dw|
anonymous
  • anonymous
oh! i see now! Gracias!
Vocaloid
  • Vocaloid
|dw:1443486079517:dw|
Vocaloid
  • Vocaloid
now add everything in black, then subtract 2
anonymous
  • anonymous
Okay. Un momento por favor! one sec
anonymous
  • anonymous
\[16x ^{4} + 4x^{3} + 4x ^{2} + 4x ^{3} + x ^{2} + x + 4x ^{2} + x + 1\]
anonymous
  • anonymous
\[16x ^{4} + 8x ^{3} + 8x ^{3} + x ^{2} +x ^{2} + 1\]
anonymous
  • anonymous
\[(16x ^{4} + 16x ^{3} + x ^{4} + 1) - 2\]
anonymous
  • anonymous
@Vocaloid
anonymous
  • anonymous
I'm probably not doing this right! But am really trying. Thanks for the help!
Vocaloid
  • Vocaloid
check your math again
anonymous
  • anonymous
what do I do from here?
Vocaloid
  • Vocaloid
|dw:1443486993727:dw|
Vocaloid
  • Vocaloid
|dw:1443487003487:dw|
Vocaloid
  • Vocaloid
|dw:1443487010986:dw|
Vocaloid
  • Vocaloid
16x^4 + 4x^3 + 4x^2 + 4x^3 + x^2 + x + 4x^2 + x + 1
anonymous
  • anonymous
How do I put it all together?
Vocaloid
  • Vocaloid
combine like terms
anonymous
  • anonymous
oh
Vocaloid
  • Vocaloid
16x^4 + 4x^3 + 4x^2 + 4x^3 + x^2 + x + 4x^2 + x + 1 = 16x^4 + 8x^3 + 9x^2 + 2x + 1 now subtract 2 = 16x^4 + 8x^3 + 9x^2 + 2x - 1
Vocaloid
  • Vocaloid
and that's your final answer
anonymous
  • anonymous
how did you get 9x^2?
anonymous
  • anonymous
oh you added 4x^2, 4x^2, and x^2! Gotcha!
anonymous
  • anonymous
Wow! Thank you so much for helping me with this problem! You are a great teacher and very patient! Gracias! Muy bien!

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