Question

I think there's a mistake on the 18.01 exercises 1A-4B) We're asked to write a function as a sum of even and odd functions. I think the second term of the function should read: (f(x)-f(-x))/2. If it's not a typo, I'm stumped...

Answer 1

Are you asking about this
http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-a-definition-and-basic-rules/problem-set-1/
?
I agree when they (try) to show G(x) is odd, they seemed to have lost a minus sign.
what they have in the solution is
\[ G(x) = \frac{1}{2} (f(x) - f(-x) )\\ G(-x) = \frac{1}{2} (f(x) - f(-x) )\]
which of course is a typo. They meant to write
\[ G(-x) = \frac{1}{2} (f(-x) - f(-(-x)) )= \frac{1}{2} (f(-x) - f(x) )\\
= - \frac{1}{2} (-f(-x) + f(x) )\\= - \frac{1}{2} (f(x)-f(-x) ) \\= -G(x)
\]

Answer 2

Yes! That's what I thought. Thanks for the confirmation.