Prove that every function defined on the real line can be written as a sum of an even and an odd
I'm not really sure where to start - any hints would be much appreciated
I'd say the first thing to do is write down the definition of an odd ad even function. It is asking to show that f(x) = g(x) + h(x) holds for even functions g(x), odd functions h(x) and even/odd functions f(x).
Hint: Try using the fact that f(x)/g(x) = 0 is an even/odd function as a first step.