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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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If \(f:R \to R\) is defined by $f(x) = x^2$ - $3x+2$. Find $f(f(x))$:

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  • Given two functions $f:A \to B $ and $g:B \to C$, then composition of $f$ and $g$, $gof:A \to C$ by $ gof (x)=g(f(x))\;for\; all \;x \in A$
Given $f(x) = x^2-3x+2$, we need to find $f(f(x))$:
$\Rightarrow f(f(x)) = f (x^2-3x+2) = (x^2-3x+2)^2 - 3(x^2-3x+2) + 2$
$\Rightarrow f(f(x)) = x^4+9x^2+4-6x^3-12x+4x^2 - 3x^2+9x-6+2 $
$\Rightarrow f(f(x)) = x^4-6x^3+10x^2-3x$
answered Feb 27, 2013 by meena.p
edited Mar 20, 2013 by balaji.thirumalai

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