2006 AMC 12A Problems/Problem 18

Problem

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 $f$ ?

$\mathrm{(A) \ } \{x|x\ne 0\}\qquad \mathrm{(B) \ } \{x|x<0\}$ $\mathrm{(C) \ } \{x|x>0\}\qquad\mathrm{(D) \ } \{x|x\ne -1\;\mathrm{and}\; x\ne 0\;\mathrm{and}\; x\ne 1\}\qquad \mathrm{(E) \ } \{-1,1\}$

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2006 AMC 12A Problems/Problem 18

Problem

Solution

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