Question 57
Let $n \in \mathbb{N}$, $n \geq 2$, and $a_1, a_2, ..., a_n \in (0, \infty)$ such that $a_1 \cdot a_2 \cdot ... \cdot a_n = 1$. Prove that the function
$$
f : (0, \infty) \to \mathbb{R}, f(x) = (1 + a_1^x) \cdot (1 + a_2^x) \cdot \dots \cdot (1 + a_n^x)
$$
is increasing.
$$
f : (0, \infty) \to \mathbb{R}, f(x) = (1 + a_1^x) \cdot (1 + a_2^x) \cdot \dots \cdot (1 + a_n^x)
$$
is increasing.