# Problem #2164

 2164 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 $f$? $\mathrm{(A) \ } \{x|x\ne 0\}\qquad \mathrm{(B) \ } \{x|x<0\}\qquad \mathrm{(C) \ } \{x|x>0\}\qquad \mathrm{(D) \ } \{x|x\ne -1\;$ $\mathrm{and}\; x\ne 0\;\mathrm{and}\; x\ne 1\}\qquad \mathrm{(E) \ } \{-1,1\}$ This problem is copyrighted by the American Mathematics Competitions.
Note: you aren't logged in. If you log in, we'll keep a record of which problems you've solved.