Question 141
A function $f: (0, +\infty) \to \mathbf{R}$ satisfies the following conditions:
a. $f(a) = 1$ for a positive real number $a$,
b. $f(x)f(y) + f(\frac{a}{x})f(\frac{a}{y}) = 2f(xy)$, for any positive real number $x, y$.
Prove that $f(x)$ is constant.
a. $f(a) = 1$ for a positive real number $a$,
b. $f(x)f(y) + f(\frac{a}{x})f(\frac{a}{y}) = 2f(xy)$, for any positive real number $x, y$.
Prove that $f(x)$ is constant.