(adsbygoogle = window.adsbygoogle || []).push({}); 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!!

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# Triangle Inequality Q

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