anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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FireKat97
  • FireKat97
I think you just simplify now, remember for \[(a + b)^2 = a^2 + 2ab + b^2\]
FireKat97
  • FireKat97
so try and simplify and post up what you get
anonymous
  • anonymous
Alright

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More answers

anonymous
  • anonymous
I'm still confused. the exponents are what I don't understand. Do I add the terms together or...
FireKat97
  • FireKat97
yup you want to add like terms together. have you tried expanding \[(2x^2 + 5)^2\]?
anonymous
  • anonymous
Expanding?
FireKat97
  • FireKat97
because it best if you have a go and I can then check and direct you
FireKat97
  • FireKat97
Yup you can expand/open them using the rule I'd shown you above
FireKat97
  • FireKat97
then we can collect like terms to simplify
anonymous
  • anonymous
Oh! Ok. Got it. Hold on a moment.
anonymous
  • anonymous
I got \[2x ^{4}+5^{2}+2x ^{2}+7\] Is that all I can do? Or can it be simplified more?
FireKat97
  • FireKat97
hm your answer doesn't quite match mine, what did you get when you expanded \[(2x^2 + 5)^2\]?
anonymous
  • anonymous
\[2x ^{4}+5^{2}\]
anonymous
  • anonymous
OH!
anonymous
  • anonymous
5squared should be 25.
FireKat97
  • FireKat97
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
anonymous
  • anonymous
Is That all we can do?
FireKat97
  • FireKat97
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
FireKat97
  • FireKat97
sorry correction from above**** "Our task is to simplify \[(2x^2 + 5)^2 + (2x + 5) + 2\]"****
anonymous
  • anonymous
\[4x ^{4}+22x ^{2}+32\] Is this right?
FireKat97
  • FireKat97
yupp thats correct @whitelynx! :D

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