[tex]\begin{gathered} \text{The function is,} \\ f(x)=x^2+2 \\ \text{The given data is}\Rightarrow f(x)=11 \\ So,\text{ } \\ \text{Substitute the value of f(11) in the function as follows:} \\ 11=x^2+2 \\ x^2=11-2 \\ x=\sqrt[]{9} \\ x=3 \\ So,\text{ the option (C) is correct.} \end{gathered}[/tex]