To do this, we can use the definition of continuity:
For any ε>0, we need to find a δ>0 such that |(f+g)(x)-(f+g)(0)|<ε whenever |x-0|<δ.
Using the triangle inequality, we have:
|(f+g)(x)-(f+g)(0)| = |f(x)+g(x)-f(0)-g(0)| ≤ |f(x)-f(0)| + |g(x)-g(0)|
Since f
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