Can a continuous function imply continuity of its absolute value?

[Chris(DE)]

Homework Statement

Prove that if f is continuous at a, then so is |f|

Homework Equations

The Attempt at a Solution

I know
lim f = L
x->a

Not sure really where to go from here.

 

[shwanky]

to prove that f is continuous at a, you must prove that $$f(a)$$ is defined, that $$\lim_{x \to a} f(x)$$ exists and that $$\lim_{x \to a} f(x) = f(a)$$.

 

[Chris(DE)]

Thanks I should be ok from here.