If $f:R \to R$ is defined by $f(x) = {x^2} - 3x + 2$, write $f\{ f(x)\}$

It is given that,, $f(x) = {x^2} - 3x + 2$

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

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

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

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

$f\{ f(x)\} = {x^4} - 6{x^3} + 10{x^2} - 3x$