1989 APMO Problems/Problem 5


Determine all functions $f$ from the reals to the reals for which

(1) $f(x)$ is strictly increasing and (2) $f(x) + g(x) = 2x$ for all real $x$,

where $g(x)$ is the composition inverse function to $f(x)$. (Note: $f$ and $g$ are said to be composition inverses if $f(g(x)) = x$ and $g(f(x)) = x$ for all real $x$.)


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