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**1. Homework Statement**

Prove: If [tex]f[/tex] is defined on [tex]\mathbb{R}[/tex] and continuous at [tex]x=0[/tex], and if [tex]f(x_{1}+x_{2})=f(x_{1})+f(x_{2})[/tex] [tex]\forall x_{1},x_{2} \in\mathbb{R}[/tex], then [tex]f[/tex] is continous at all [tex]x\in\mathbb{R}[/tex].

**2. Homework Equations**

None

**3. The Attempt at a Solution**

Need a pointer to get started. Cannot wrap my head around it. I understand that I need to prove that the sum of two continuous functions is continous also.

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