anonymous
  • anonymous
Let f(x) = 3x^2 – x + 2 and g(x) = 5x^2 – 1. Find f(g(x)). Please explain it to me as well! Thanks :)
Mathematics
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SOLVED
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chestercat
  • chestercat
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welshfella
  • welshfella
f(g(x)) - work for the ' inside out'. g(x) replaces the x in f(x)
welshfella
  • welshfella
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anonymous
  • anonymous
so, f(x) = 3x^2 – x + 2 and g(x) = 5x^2 – 1 becomes: f(x) = 3(5x^2 – 1)^2 – 5x^2 – 1 + 2

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More answers

welshfella
  • welshfella
yes you are on the way but put parentheses around the 5x^2 - 1
welshfella
  • welshfella
- otherwise you'll get your signs wrong
anonymous
  • anonymous
f(x) = 3(5x^2 – 1)^2 – (5x^2 – 1) + 2?
welshfella
  • welshfella
and its f(g(x)) not f(x)
welshfella
  • welshfella
yes
anonymous
  • anonymous
ohhh okay okay so f(g(x)) = 3(5x^2 – 1)^2 – 5x^2 – 1 + 2
welshfella
  • welshfella
no - you have to distribute the - over the parentheses so its -5x2 + 1
anonymous
  • anonymous
@welshfella after this question can you please help me?
welshfella
  • welshfella
- (5x^2 - 1) = -5x^2 + 1
anonymous
  • anonymous
i meant to type that but i hit copy and paste and put the old equation, sorry
anonymous
  • anonymous
f(g(x)) = 3(5x^2 – 1)^2 – 5x^2 + 1 + 2
anonymous
  • anonymous
then do i just solve normally?
welshfella
  • welshfella
yes but i guess they want you to expand that now 3(5x^2 - 1)^2 = 3(25x^4 -10x^2 + 1)
welshfella
  • welshfella
then simplify 3(25x^4 -10x^2 + 1) - 5x^2 + 3 = 75x^4 - 30x^2 + 3 - 5x^2 + 3 combine like terms then thats it
anonymous
  • anonymous
3(5x^2 - 1)^2 expand: 3(25x^4 -10x^2 + 1) simplify: 3(25x^4 -10x^2 + 1) - 5x^2 + 3 = 75x^4 - 30x^2 + 3 - 5x^2 + 3 that's all? not as hard as i thought. thank you!
welshfella
  • welshfella
yw

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