Show that if $f \in \mathbf{Q}\llbracket x \rrbracket$ is the power series expansion of a rational function with rational coefficients, then $f$ is globally bounded.
(A power series $f(x) = \sum_{n=0}^{\infty} c_n x^n \in \mathbf{Q}\llbracket x \rrbracket$ is globally bounded if there exist integers $A, B \geq 1$ such that $A f(Bx) \stackrel{\text{def}}{=} \sum_{n=0}^{\infty} (B^n A c_n) x^n$ is a power series with integer coefficients.)