f+ is the even part of the function and f- is the odd part. I'm not able to understand how it is that they got the values of modulus of x and x for the even and odd parts of the function respectively.
For the even part, I think it might be because f(x) would be reflected in the y-axis but then for the even part shouldn't we have modulus of 2x instead of modulus of x?
For the odd part I have no idea how they got it to be x.
Any help would be much appreciated.
For a general function $f$, you can find the odd and even parts as follows:
If $f(x) = f^+(x) + f^-(x)$, then $f(-x) = f^+(x) - f^-(x)$ (by properties of even/oddness).
Then
$$ \frac12(f(x) + f(-x)) = f^+(x) $$
and
$$ \frac12(f(x) - f(-x)) = f^-(x). $$