A function $f$ is considered a bounded function on $A$ if there is a certain value $M > 0$ such that $|f(x)| \leq M$ for all $x \in A$. Let $g$ be a function with domain $A$ and $f$ be a bounded function on $A$. Prove that if $\displaystyle\lim_{x \rightarrow c} g(x)

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