Question:
If $f \mathbf{R} \rightarrow \mathbf{R}$ is defined bv $f(x)=x^{2}-3 x+2$ find $f(f(x))$
Solution:
It is given that $f: \mathbf{R} \rightarrow \mathbf{R}$ is defined as $f(x)=x^{2}-3 x+2$
$f(f(x))=f\left(x^{2}-3 x+2\right)$
$=\left(x^{2}-3 x+2\right)^{2}-3\left(x^{2}-3 x+2\right)+2$
$=x^{4}+9 x^{2}+4-6 x^{3}-12 x+4 x^{2}-3 x^{2}+9 x-6+2$
$=x^{4}-6 x^{3}+10 x^{2}-3 x$