An exercise in my assignment asks for the following proof.
Prove that the vector space R->R is equal to the direct sum of:
the set of real valued even functions on R Ue
the set of real valued odd functions on R Uo
Investigating this question I seem to have found a counter example f(x)= e^x.
This is because f(-x) = 1/e^x which is neither even or odd.
Can someone please clarify if I'm mistaken or if the exercise is wrong?