Janu16
  • Janu16
Let f(x) = 3x^2 – x + 2 and g(x) = 5x^2 – 1. Find f(g(x)). Show each step of your work.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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Janu16
  • Janu16
@peachpi
IrishBoy123
  • IrishBoy123
\( g(x) = 5x^2 – 1\) \(f(x) = 3x^2 – x + 2\) \(f[g(x)] = f(5x^2 – 1) = 3[5x^2 – 1]^2 – [5x^2 – 1] + 2 \) this what you meant?? hope it helps :p
jdoe0001
  • jdoe0001
\(\bf f(x)=3x^2-x+2\qquad g(x)={\color{brown}{ 5x^2-1 }} \\ \quad \\ f(\ {\color{brown}{ g(x)}}\ )=3x({\color{brown}{ g(x)}})^2-({\color{brown}{ g(x)}})+2 \\ \quad \\ f(\ {\color{brown}{ g(x)}}\ )=3x({\color{brown}{ 5x^2-1}})^2-({\color{brown}{ 5x^2-1}})+2\)

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Janu16
  • Janu16
so do you sole this?
jdoe0001
  • jdoe0001
just distribute and simplify, sure
Janu16
  • Janu16
25x^2-3x^2+25x^2-3^2+2?
jdoe0001
  • jdoe0001
hmm, notice, the 1st term has an squared binomial you need to expand that one first
jdoe0001
  • jdoe0001
\(\bf f(\ {\color{brown}{ g(x)}}\ )=3x({\color{brown}{ 5x^2-1}})^2-({\color{brown}{ 5x^2-1}})+2 \\ \quad \\ f(g(x))=3x({\color{brown}{ 25x^4-10x^2+1}})-5x^2+1+2\)
Janu16
  • Janu16
why x4
Janu16
  • Janu16
@jdoe0001
jdoe0001
  • jdoe0001
\(\bf (5x^2-1)^2\iff (5x^2-1)(5x^2-1)\implies (25x^4-10x^2+1)\)
jdoe0001
  • jdoe0001
you can FOIL if you want
Janu16
  • Janu16
ojok

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