If f : z → z is defined by f ( x ) = x 9 - 11 x 8 - 2 x 7 + 22 x 6 + x 4 - 12 x 3 + 11 x 2 + x - 3…

Given, 

 $f\left(x\right)=x^9-11x^8-2x^7+22x^6+x^4-12x^3+11x^2+x-3 \forall x\in z$

Putting $11$ in place of $x$ and solving the equation

$f\left(11\right)={11}^9-11{\left(11\right)}^8-2{\left(11\right)}^7+22{\left(11\right)}^6 -{\left(11\right)}^4-12{\left(11\right)}^3-11{\left(11\right)}^2+\left(11\right)-3$

$=11-3$

$=8$