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# If $f:R \to R$ is defined by $f(x) = x^2$ - $3x+2$. Find $f(f(x))$:

Toolbox:
• 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 $f(f(x))$:
$\Rightarrow f(f(x)) = f (x^2-3x+2) = (x^2-3x+2)^2 - 3(x^2-3x+2) + 2$
$\Rightarrow f(f(x)) = x^4+9x^2+4-6x^3-12x+4x^2 - 3x^2+9x-6+2$
$\Rightarrow f(f(x)) = x^4-6x^3+10x^2-3x$
edited Mar 20, 2013