True/False: If f and g are differentiable at some point a ∈ R, then the function f ◦ g is also differentiable at a.

Question

Statement: "If f and g are differentiable at some point a ∈ R, then the function f ◦ g is also differentiable at a."

Answer 1

f(x) = sqrt(x) <--- is continuous on x>=0

g(x) = x-8 is continuous everywhere

f(g(x)) = sqrt(x-8) <--- is continuous on x>=8

the statement is false for a=4