Question

If $f:R\to R$ is defined by $f\left(x\right)=x^2-3x+2$, find $f\left(f\right(x\left)\right)$

Answer 1

$f\left(x\right)=x^2-3x+2$

$f\left(f\left(x\right)\right)=f(x^2-3x+2)$

$f(x^2-3x+2)={(x^2-3x+2)}^2-3(x^2-3x+2)+2$

$=x^4+9x^2+4-6x^3-12x+4x^2-3x^2+9x-6+2$

$=x^4-6x^3+10x^2-3x$