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What is a "function defined on the real line"?

Is it simply a function $f(x)$ where all values of $x$ are defined?

In other words, $x+1$ is such a function, but $\frac1x$ is not since it is not defined for $0$?

Also, I'm to prove that such a function can be written as a sum of both even and odd function. Is this in the form of $f(x) = g(x)+h(x) = (g+h)(x),$ where $g$ is an even function and $h$ is an odd function?

I'm not looking for proof, as I'm to work that out on my own, but am I correct in interpreting the question, or have I missed something?

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yes. you are correct. –  voldemort Jan 17 at 15:56
    
But note that the property of decompose a function in odd and even parts, is a local property, i.e. it only depends on the point $x\in \mathbb{R}$, so it also is valid for any function defined in any subset of the real line. –  Tomás Jan 17 at 16:18

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