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.

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- Apr 16th 2007, 01:12 PMslowcurv99proof 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. - Apr 16th 2007, 01:18 PMPlato
For part A just see that: ||f(x)|-|f(c)||

__<__|f(x)-f(c)|.

Review part B; can’t read it. - Apr 16th 2007, 01:20 PMslowcurv99
sorry, that funky word is suppose to say continuous

- Apr 16th 2007, 01:26 PMPlato
Consider F(x)=-1 if x<0 and F(x)=1 if x

__>__0.

Is |F| continuous at 0?