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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!

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  1. Vocaloid
    • one year ago
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    g(f(x)) means take f(x) and substitute it for x in g(x)

  2. Vocaloid
    • one year ago
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    g(x) = x^2 - 2 g(f(x)) = f(x)^2 - 2 = (4x^2 + x + 1)^2 - 2 finish by expanding

  3. jdoe0001
    • one year ago
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    actaully it was the other way around... anyhow =)

  4. anonymous
    • one year ago
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    i'm confused now. what do you mean the other way around?

  5. jdoe0001
    • one year ago
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    \(\bf f(x) ={\color{brown}{ 4x^2+x+1}}\qquad g(x)={\color{black}{ x^2-2}} \\ \quad \\ g(\ {\color{brown}{ f(x)}}\ )=({\color{brown}{ f(x)}})^2-2\)

  6. jdoe0001
    • one year ago
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    expand as Vocaloid suggested

  7. anonymous
    • one year ago
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    okay... so g(f(x)) = (4x^2 + x + 1)^2 - 2. I'm probably way off, but 16x^4 + x^2 + 2 - 2.

  8. jdoe0001
    • one year ago
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    just bear in mind that \(\bf (4x^2 + x + 1)^2 \implies (4x^2 + x + 1)(4x^2 + x + 1)\)

  9. anonymous
    • one year ago
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    so was I right? I just had to take away the -2 at the end?

  10. anonymous
    • one year ago
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    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.

  11. Vocaloid
    • one year ago
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    not quite (4x^2 + x + 1)^2 = (4x^2 + x + 1)*(4x^2 + x + 1) use foil to expand

  12. anonymous
    • one year ago
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    Okay. Foil = First, outer, inner, last?

  13. Vocaloid
    • one year ago
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    yes

  14. Vocaloid
    • one year ago
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    we also have a middle term in this case, x

  15. anonymous
    • one year ago
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    a sec. pls

  16. anonymous
    • one year ago
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    so it would be x squared in the middle

  17. Vocaloid
    • one year ago
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    |dw:1443485986922:dw|

  18. Vocaloid
    • one year ago
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    |dw:1443486003860:dw|

  19. Vocaloid
    • one year ago
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    |dw:1443486036186:dw|

  20. anonymous
    • one year ago
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    oh! i see now! Gracias!

  21. Vocaloid
    • one year ago
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    |dw:1443486079517:dw|

  22. Vocaloid
    • one year ago
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    now add everything in black, then subtract 2

  23. anonymous
    • one year ago
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    Okay. Un momento por favor! one sec

  24. anonymous
    • one year ago
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    \[16x ^{4} + 4x^{3} + 4x ^{2} + 4x ^{3} + x ^{2} + x + 4x ^{2} + x + 1\]

  25. anonymous
    • one year ago
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    \[16x ^{4} + 8x ^{3} + 8x ^{3} + x ^{2} +x ^{2} + 1\]

  26. anonymous
    • one year ago
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    \[(16x ^{4} + 16x ^{3} + x ^{4} + 1) - 2\]

  27. anonymous
    • one year ago
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    @Vocaloid

  28. anonymous
    • one year ago
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    I'm probably not doing this right! But am really trying. Thanks for the help!

  29. Vocaloid
    • one year ago
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    check your math again

  30. anonymous
    • one year ago
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    what do I do from here?

  31. Vocaloid
    • one year ago
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    |dw:1443486993727:dw|

  32. Vocaloid
    • one year ago
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    |dw:1443487003487:dw|

  33. Vocaloid
    • one year ago
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    |dw:1443487010986:dw|

  34. Vocaloid
    • one year ago
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    16x^4 + 4x^3 + 4x^2 + 4x^3 + x^2 + x + 4x^2 + x + 1

  35. anonymous
    • one year ago
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    How do I put it all together?

  36. Vocaloid
    • one year ago
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    combine like terms

  37. anonymous
    • one year ago
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    oh

  38. Vocaloid
    • one year ago
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    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

  39. Vocaloid
    • one year ago
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    and that's your final answer

  40. anonymous
    • one year ago
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    how did you get 9x^2?

  41. anonymous
    • one year ago
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    oh you added 4x^2, 4x^2, and x^2! Gotcha!

  42. anonymous
    • one year ago
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    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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