1. The problem statement, all variables and given/known data Part of an [itex]\epsilon-\delta[/itex] 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: [itex]|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)|[/itex] using the triangle inequality. Is that valid? Thanks!!