# If f: R → R is defined by f(x) = x2 − 3x + 2, find f(f(x)).

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

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

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

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

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