Epsilon-Delta Proof for Continuity of f + 2g at x = a

[rudders93]

Homework Statement

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

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!

 

[vela]

Sure. Why not?