Question

I believe there is a typo on the Problem Set 1 question 1A-4 (b). The second function has:
f(x)+f(-x) in the numerator.

The result of this is different than the question intends. Am I correct?

Answer 1

Good find on the typo. There are quite a few typos scattered throughout the problem sets. I wish there was an errata page we could post to. As indicated in the solutions, the equation should have read
\[ f(x) = \frac{f(x)+ f(-x)}{2} + \frac{f(x) - f(-x)}{2}\]

Answer 2

You are correct, and they actually write it correctly in the solution, but the solution to that is slightly confusing as well (at least to me) and would have been clearer written out like:

\[G(x) = \frac{ f(-x)-f(-(-x)) }{ 2 }\]\[= \frac{f(-x)-f(x)}{2}\]\[= \frac{-(f(x)-f(-x))}{2}\]\[= -\left( \frac{f(x)-f(-x)}{2} \right) = -G(x)\]