Yes.

If f(x)>=0 is continous.

Then, sqrt(f(x)) is continous.

Then,

sqrt(f^2)=|f| is continous.

But if |f| is contonous it must be that f was continous.

False.B) If f is continuous on D, then f(D) is a bounded subset

Consider,

1/x on (0,1)

I have an elegant approach to this one.C) if f and g are not continuous on D, then f + g is not continuous on D