1. The problem statement, all variables and given/known data V is the set of functions R -> R; pointwise addition and (a.f)(x) = f(ax) for all x. is V a vector space given the operations? 2. Relevant equations nil. 3. The attempt at a solution i think it is not closed under multiplication. if r is an element of R, then r*a(x) . r*f(x) = (r^2)*(a.f)(x) which is not equal to r*f(ax) im not really sure if i even have the correct approach. any help would be greatly appreciated. thanks!