Thread: proof of continuity

A) Let f: D -> R and define |f|: D->R by |f|(x) = |f(x)|. Suppose that f is continuous at c element of D. Prove that |f| is continuous at C

B) if |f| os cpmtomipis at c. does it follow that f is continuous at c? Justify your answer.

For part A just see that: ||f(x)|-|f(c)||<|f(x)-f(c)|.

Review part B; can’t read it.

sorry, that funky word is suppose to say continuous

Consider F(x)=-1 if x<0 and F(x)=1 if x>0.
Is |F| continuous at 0?