jmc

The function $f$ has the property that for each real number $x$ in its domain, $1/x$ is also in its domain and $$f(x)+f\left(\frac{1}{x}\right)=x.$$What is the largest set of real numbers that can be in the domain of $f$?

(a) $\{x\mid x\ne 0\}$

(b) $\{x\mid x<0\}$

(c) $\{x\mid x>0\}$

(d) $\{x\mid x\ne -1\text{and}x\ne 0\text{and}x\ne 1\}$

(e) $\{-1,1\}$