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anonymous
 one year ago
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!
anonymous
 one year ago
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!

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Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2g(f(x)) means take f(x) and substitute it for x in g(x)

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2g(x) = x^2  2 g(f(x)) = f(x)^2  2 = (4x^2 + x + 1)^2  2 finish by expanding

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0actaully it was the other way around... anyhow =)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i'm confused now. what do you mean the other way around?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\bf f(x) ={\color{brown}{ 4x^2+x+1}}\qquad g(x)={\color{black}{ x^22}} \\ \quad \\ g(\ {\color{brown}{ f(x)}}\ )=({\color{brown}{ f(x)}})^22\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0expand as Vocaloid suggested

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay... so g(f(x)) = (4x^2 + x + 1)^2  2. I'm probably way off, but 16x^4 + x^2 + 2  2.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0just bear in mind that \(\bf (4x^2 + x + 1)^2 \implies (4x^2 + x + 1)(4x^2 + x + 1)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so was I right? I just had to take away the 2 at the end?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What 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
 one year ago
Best ResponseYou've already chosen the best response.2not quite (4x^2 + x + 1)^2 = (4x^2 + x + 1)*(4x^2 + x + 1) use foil to expand

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay. Foil = First, outer, inner, last?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2we also have a middle term in this case, x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so it would be x squared in the middle

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443485986922:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443486003860:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443486036186:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh! i see now! Gracias!

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443486079517:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2now add everything in black, then subtract 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay. Un momento por favor! one sec

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[16x ^{4} + 4x^{3} + 4x ^{2} + 4x ^{3} + x ^{2} + x + 4x ^{2} + x + 1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[16x ^{4} + 8x ^{3} + 8x ^{3} + x ^{2} +x ^{2} + 1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(16x ^{4} + 16x ^{3} + x ^{4} + 1)  2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm probably not doing this right! But am really trying. Thanks for the help!

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2check your math again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what do I do from here?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443486993727:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443487003487:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443487010986:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.216x^4 + 4x^3 + 4x^2 + 4x^3 + x^2 + x + 4x^2 + x + 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How do I put it all together?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.216x^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
 one year ago
Best ResponseYou've already chosen the best response.2and that's your final answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how did you get 9x^2?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh you added 4x^2, 4x^2, and x^2! Gotcha!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow! 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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