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anonymous

  • one year ago

PLEASE HELP!!! Let f(x) = 3x^2 – x + 2 and g(x) = 5x2 – 1. Find f(g(x)).

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  1. anonymous
    • one year ago
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    @ganeshie8 @robtobey

  2. anonymous
    • one year ago
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    is it 5x^2-1 or 5x=2-1?

  3. anonymous
    • one year ago
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    5x+2-1

  4. anonymous
    • one year ago
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    sorry it's g(x) = 5x^2 - 1

  5. anonymous
    • one year ago
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    oh okay

  6. anonymous
    • one year ago
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    are you looking for where they intersect

  7. anonymous
    • one year ago
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    ?

  8. anonymous
    • one year ago
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    no I'm looking for f(g(x))

  9. anonymous
    • one year ago
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    whats F(g(x))?

  10. anonymous
    • one year ago
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    I'm not sure, which is why I need help

  11. anonymous
    • one year ago
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    oh

  12. Jhannybean
    • one year ago
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    take your function, \(f(\color{red}{x}) = 3\color{red}{x^2}-\color{red}{x}+2\) and replace every red colored x with \(\color{red}{5x^2-1}\)

  13. Jhannybean
    • one year ago
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    Simplify that and you will have \(f(g(x))\)

  14. anonymous
    • one year ago
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    okay, let me work this out

  15. Jhannybean
    • one year ago
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    There was a typo, haha. \[f(g(x)) = 3(5x^2-1)^2 -(5x^2-1) +2\]

  16. anonymous
    • one year ago
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    Refer to the attachment from the Mathematica program.

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  17. anonymous
    • one year ago
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    okay, I think I worked it out. is the answer f(g(x)) = 25x^4 - 6 ?!?!

  18. Jhannybean
    • one year ago
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    \[f(g(x)) = 3( 24x^4-10x^2+1) -5x^2+1+2\]\[f(g(x)) = 72x^4 -30x^2+3-5x^2+3\]\[f(g(x))= 72x^4-(30+5)x^2+6\]\[\boxed{\color{red}{f(g(x)) = 72x^4 -35x^2+6}}\]

  19. Jhannybean
    • one year ago
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    I think you made a mistake expanding \((5x^2-1)^2\)

  20. anonymous
    • one year ago
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    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

  21. anonymous
    • one year ago
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    @Jhannybean ?!

  22. Jhannybean
    • one year ago
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    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 \((a-b)^2\)

  23. Jhannybean
    • one year ago
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    Are you with me so far?

  24. anonymous
    • one year ago
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    oh. but then shouldn't it be f(g(x)) = 75x^4 - 30x^2 + 3 − 5x^2 + 1 + 2 instead of having 72x^4?

  25. anonymous
    • one year ago
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    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

  26. Jhannybean
    • one year ago
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    Oh yes it was my fault. I found it. I wrote 24 instead of 25. You are right. It should be 75 ^^

  27. Jhannybean
    • one year ago
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    \[f(g(x)) = 3( \color{blue}{24x^4}-10x^2+1) -5x^2+1+2\] SO when I was solving it I got 72x\(^4\) instead of 75x\(^4\)

  28. anonymous
    • one year ago
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    oh, so the answer is f(g(x)) = 75x^4 - 35x^2 + 6?

  29. Jhannybean
    • one year ago
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    Yep.

  30. anonymous
    • one year ago
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    thanks :)

  31. Jhannybean
    • one year ago
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    Good job on spotting that error.

  32. anonymous
    • one year ago
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    lol thanks

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