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If $f: R \rightarrow R$ is defined by $f(x)=x^2-3 x+2$, find $f(f(x))$.
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Verified Answer
$\quad f(x)=x^2-3 x+2$
$f(f(x))=[f(x)]^2-3(f(x))+2$
$=\left(x^2-3 x+2\right) 2-3\left(x^2-3 x+2\right)+2$
$=x^4+9 x^2+4-6 x^3-12 x+4 x^2-3 x^2+9 x-6+2$
$=x^4-6 x^3+10 x^3-3 x$
$f(f(x))=[f(x)]^2-3(f(x))+2$
$=\left(x^2-3 x+2\right) 2-3\left(x^2-3 x+2\right)+2$
$=x^4+9 x^2+4-6 x^3-12 x+4 x^2-3 x^2+9 x-6+2$
$=x^4-6 x^3+10 x^3-3 x$
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