when we can say that $\limsup_{n\to\infty}f(a_n)=f(\limsup_{n\to\infty}a_n)$?

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when we can say that $\limsup_{n\to\infty}f(a_n)=f(\limsup_{n\to\infty}a_n)$? (What conditions must have the function $f$?)