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funtowrite
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. "
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.
Thank you! I think I understand it now :)