What condition on a function at the point guarantees that whenever ?

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

What condition on a function

f

at the point

L

guarantees that

\displaystyle \lim_{x\to a} f\bigl(g(x)\bigr)=f\!\left(\lim_{x\to a} g(x)\right)

whenever

\displaystyle \lim_{x\to a} g(x)=L