question_answer

Let f : \[R\to R:f(x)=({{x}^{2}}-3x+2).\] Find fof(x).

Answer:

\[fof(x)=f\{f(x)\}=f\{{{x}^{2}}-3x+2\}\]                         \[={{({{x}^{2}}-3x+2)}^{2}}-3({{x}^{2}}-3x+2)+2\]      \[={{x}^{4}}+9{{x}^{2}}+4-6{{x}^{3}}-12x+4{{x}^{2}}-3{{x}^{2}}\]                                                                \[+9x-6+2\]                         \[={{x}^{4}}-6{{x}^{3}}+10{{x}^{2}}-3x\]