anonymous
  • anonymous
Let f(x) = 3x2 – x + 2 and g(x) = 5x2 – 1. Find f(g(x)). Show each step of your work
Mathematics
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anonymous
  • anonymous
Let f(x) = 3x2 – x + 2 and g(x) = 5x2 – 1. Find f(g(x)). Show each step of your work
Mathematics
chestercat
  • chestercat
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mathstudent55
  • mathstudent55
First, write out f(x)
mathstudent55
  • mathstudent55
|dw:1437453923911:dw|
mathstudent55
  • mathstudent55
Now replace x in the equation above by what g(x) is equal to, which is 5x^2 - 1.

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mathstudent55
  • mathstudent55
|dw:1437453998789:dw|
mathstudent55
  • mathstudent55
Now simplify.
mathstudent55
  • mathstudent55
|dw:1437454056943:dw|
mathstudent55
  • mathstudent55
I left out one close-parenthesis above, so I just added it.
anonymous
  • anonymous
Great explanation but there's a small mistake. final answer should be like 3(5x^2-1)^2 -(5x^2-1)+2
mathstudent55
  • mathstudent55
Thanks, I forgot the square of the first term. |dw:1437456208250:dw|
anonymous
  • anonymous
Wouldn't you also have to multiply the first x value by three after squaring it? Or would the answer just be left as is?
anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous
(75x^4-30x^2+3)-(5x^2-1)+2?
mathstudent55
  • mathstudent55
\(f(g(x)) = 3(5x^2 - 1)^2 - (5x^2 - 1) + 2\) \(f(g(x)) = 3(25x^4 - 10x^2 + 1) - 5x^2 + 1 + 2\) \(f(g(x)) = 75x^4 - 30x^2 + 3 - 5x^2 + 3\) \(f(g(x)) = 75x^4 - 35x^4 + 6\)

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