# Limit of monotic transformation

## Main Question or Discussion Point

Hello, I was just wondering if is it true that the limit of a monotonic transformation of a function is the same as the monotonic transformation of its limit? That is, does

$$\lim_{n \rightarrow a} f(g(x)) = f(\lim_{n \rightarrow a} g(x))$$

for monotonic $$f$$, some $$a$$, and such that if the limit does not exist for one side of the expression, it doesn't exist for both?

Thanks.

mathman
Your original equation does not describe the dependence on n of anything.

Sorry, replace n with x - was very tired!

Correction: $$\lim_{x \rightarrow a} f(g(x)) = f(\lim_{x \rightarrow a} g(x))$$

mathman