Let f: D-->R and define |f|:D-->R by |f|(x)=|f(x)|. Suppose that f is continuous at c belonging to D. Prove

Let f: D--%26gt;R and define |f|:D--%26gt;R by |f|(x)=|f(x)|. Suppose that f is continuous at c belonging to D. Prove that |f| is continuous at c.

Let f: D--%26gt;R and define |f|:D--%26gt;R by |f|(x)=|f(x)|. Suppose that f is continuous at c belonging to D. Prove
let epsilon %26gt;0


we want to find a delta%26gt;0 such that


|x-c|%26lt;delta =%26gt; | |f(x)| - |f(c)| | %26lt; epsilon











since f is continuous, then there exist a delta%26gt;0 such that


|x-c| %26lt; delta =%26gt; |f(x) -f(c) |%26lt; epsilon


but | |f(x)| - |f(c)| | %26lt;= |f(x) -f(c) |.
Reply:What math is this? Sorry, I can't help.