# What is a “function defined on the real line”?

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 '14 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 '14 at 16:18
I dunno, I find the idea of, say, $\sqrt x$ as being "the sum of an even function and an odd function" to be rather repulsive. – Eric Stucky Nov 19 at 16:54