Hi, can someone explain how to work through pset1 question 1A-4 b)? Thanks!
The question is:
" b) Generalize part (a) to an arbitrary function f(x) by writing
f(x)= [f(x)+ f(−x)]/2+ [f(x)+ f(−x)]/2
Verify this equation, and then show that the two functions on the right are respectively even and odd. "

Question

anonymous · Answer

There seems to be a mistake in the original assignment. If you check the solutions, you will find that the suggested equation is actually $$f(x) = [f(x)+ f(-x)] / 2 + [f(x) - f(-x)]/2$$. In fact, if you simplify the equation originally given, you will get f(x) = [2f(x) +2f(-x)]/2= f(x) + f(-x). That is, 0=f(-x), which is not true in general. Hope that helps.

anonymous · Answer

Thank you! I think I understand it now :)