Question 95
$f(x)$ is a real-valued function defined on the positive reals such that
(1) if $x \lt y$, then $f(x) \lt f(y)$;
(2) $f\left(\frac{2xy}{x+y}\right) = \frac{f(x)+f(y)}{2}$ for all $x$.
Show that $f(x) \lt 0$ for some value of $x$.
(1) if $x \lt y$, then $f(x) \lt f(y)$;
(2) $f\left(\frac{2xy}{x+y}\right) = \frac{f(x)+f(y)}{2}$ for all $x$.
Show that $f(x) \lt 0$ for some value of $x$.