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## 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

[tex]\lim_{n \rightarrow a} f(g(x)) = f(\lim_{n \rightarrow a} g(x))[/tex]

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

Thanks.

[tex]\lim_{n \rightarrow a} f(g(x)) = f(\lim_{n \rightarrow a} g(x))[/tex]

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

Thanks.