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?
Best Answer
Yes; "a function defined on the real line" is a function $f(x)$ that is defined for all real values of $x$.