Which one of the following isnot true always?

Options

A. if f(x) is not continuous at x=a,then it is not differentiable at x=a
B. If fx is continuous at x= a,then it is differentiable at x=a
C. If f(x ) and gx are differentiable at x=a,then f(x +gx )is also differentiable at x=a
D. If a function f(x is continuous at x=a,then `lim_(xtoa) f(x)` exists