For $n\in\mathbb{N}$, let $a_1,a_2,\ldots,a_n$ and $b_1,b_2,\ldots,b_n$ to be positive real numbers.
Prove that for function $f:\mathbb{R}\rightarrow\mathbb{R}$ defined as $$ f(x)=a_1 \cos(b_1 x) + \dots + a_n \cos(b_n x) $$ there exists at least one $x_0$ such as $f(x_0)=0$.