Let a function $f(x)$, and $x$ not equal to zero be such that:
$f(x)+f(1/x)=f(x)\cdot f(1/x)$ then $f(x)$ is ?

I tried differentiating it but did not find any useful outcome.
answer given at back of book is

A)$1+x^n$, $n$ belongs to $\mathbb R$

B)$1-x^n$, $n$ belongs to $\mathbb R$

C)$\pi/(2\arctan|x|)$

D)$2/(1+k\ln|x|) $