Function f(x)=(≤ft(1+2^x)^9)/(2^x) is :

$f(-x)=\frac{\left(1+2^{-x}\right)^9}{2^{-x}}=\frac{\left(2^x+1\right)^9}{\left(2^x\right)^8} \neq f(x)$ or $-f(x)$

Hence f(x) is neither even nor odd

Hence (3) is the correct answer.