# Triangle Inequality Q

1. Aug 19, 2011

### rudders93

1. The problem statement, all variables and given/known data

Part of an $\epsilon-\delta$ proof about whether or not f + 2g is continuous at x = a provided that f and g are continuous at x = a

3. The attempt at a solution

I've got the proof (I hope), but I'm uncertain about whether I can do the following:

$|f(x)+2g(x)-(f(a)+2g(a))| = |f(x)-f(a)+2g(x)-2g(a)| \leq |f(x)-f(a)| + 2|g(x)-g(a)|$ using the triangle inequality.

Is that valid?

Thanks!!

2. Aug 19, 2011

### vela

Staff Emeritus
Sure. Why not?