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anonymous

  • one year ago

Let f(x) = x2 + x + 2 and g(x) = 2x2 + 5. Find f(g(x)). Show each step of your work. I put them together for (2x2+5)2+( 2x2+5)+2. Now I'm stuck.

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  1. FireKat97
    • one year ago
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    I think you just simplify now, remember for \[(a + b)^2 = a^2 + 2ab + b^2\]

  2. FireKat97
    • one year ago
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    so try and simplify and post up what you get

  3. anonymous
    • one year ago
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    Alright

  4. anonymous
    • one year ago
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    I'm still confused. the exponents are what I don't understand. Do I add the terms together or...

  5. FireKat97
    • one year ago
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    yup you want to add like terms together. have you tried expanding \[(2x^2 + 5)^2\]?

  6. anonymous
    • one year ago
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    Expanding?

  7. FireKat97
    • one year ago
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    because it best if you have a go and I can then check and direct you

  8. FireKat97
    • one year ago
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    Yup you can expand/open them using the rule I'd shown you above

  9. FireKat97
    • one year ago
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    then we can collect like terms to simplify

  10. anonymous
    • one year ago
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    Oh! Ok. Got it. Hold on a moment.

  11. anonymous
    • one year ago
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    I got \[2x ^{4}+5^{2}+2x ^{2}+7\] Is that all I can do? Or can it be simplified more?

  12. FireKat97
    • one year ago
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    hm your answer doesn't quite match mine, what did you get when you expanded \[(2x^2 + 5)^2\]?

  13. anonymous
    • one year ago
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    \[2x ^{4}+5^{2}\]

  14. anonymous
    • one year ago
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    OH!

  15. anonymous
    • one year ago
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    5squared should be 25.

  16. FireKat97
    • one year ago
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    not quite, so we have \[(2x^2 + 5)^2\] and using \[(a + b)^2 = a^2 + 2bc + b^2\] we should get \[(2x^2)^2 + 2(2x^2)(5) + 5^2\] which simplifies down to \[4x^4 + 20x^2 + 25\] when we expand

  17. anonymous
    • one year ago
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    Is That all we can do?

  18. FireKat97
    • one year ago
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    no, we'e simplified the \[(2x^2 + 5)^2\] part, but don't forget, our task is to simplify \[(2x^2 + 5) + (2x^2 + 5) + 2\] so now we have \[4x^4 + 20x^2 + 25 + (2x^2 + 5) + 2\] so now you gotta collect like terms, try this and show me what you get @Whitelynx

  19. FireKat97
    • one year ago
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    sorry correction from above**** "Our task is to simplify \[(2x^2 + 5)^2 + (2x + 5) + 2\]"****

  20. anonymous
    • one year ago
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    \[4x ^{4}+22x ^{2}+32\] Is this right?

  21. FireKat97
    • one year ago
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    yupp thats correct @whitelynx! :D

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