Q.Which of the following function is neither even nor odd ?

Check $f(-x)$ against $f(x)$ and $-f(x)$; only $x^3+5$ matches neither, so it is neither even nor odd.

Recall: even $\Rightarrow f(-x)=f(x)$; odd $\Rightarrow f(-x)=-f(x)$.

• (a) $f(x)=x^{10}$: $f(-x)=x^{10}=f(x)$ — even.
• (c) $f(x)=x^{2}$: $f(-x)=x^{2}=f(x)$ — even.
• (d) $f(x)=x^{5}$: $f(-x)=-x^{5}=-f(x)$ — odd. …