Question 133
Let $n$ be a natural number with $n \ge 2$, and let $a_1, a_2, \dots, a_n \in (1, \infty)$ be $n$ real numbers. Prove that the function $f: [0, \infty) \to \mathbb{R}$, defined by
$$
f(x) = (a_1 a_2 \dots a_n)^x - a_1^x - a_2^x - \dots - a_n^x,
$$
for any $x \in [0, \infty)$, is strictly increasing.
$$
f(x) = (a_1 a_2 \dots a_n)^x - a_1^x - a_2^x - \dots - a_n^x,
$$
for any $x \in [0, \infty)$, is strictly increasing.