Question 88
Let $a$, $b$, $c$ be three positive real numbers. Prove that the function $f: \mathbb{R} \to \mathbb{R}$, $f(x) = \frac{a^x}{b^x + c^x} + \frac{b^x}{a^x + c^x} + \frac{c^x}{a^x + b^x}$ is increasing on $[0, \infty)$ and decreasing on $(-\infty, 0]$.