1. The problem statement, all variables and given/known data Which of the following subsets of the vector space R^R of all functions from R to R are subspaces? (proofs or counterexamples required) U:= f [tex]\in[/tex]R^R, f is differentiable and f'(0) = 0 V:= f[tex]\in[/tex]R^R, f is polynomial of the form f=at^2 for some a[tex]\in[/tex]R = There exists a of the set R: for all s of R: f(s) = as^2 W:= " " f is polynomial of the form f=at^i for some aof the set R and i of the set N = there exists i of N, there exists a of R: that for all s of R: f(s) = as^i X:= " " f is odd (f is odd such that f(-s) =-f(s) for all s of R 2. Relevant equations 3. The attempt at a solution Okay so i want to start with , odd functions. I can use the sine function as a counterexample because i don't think X is a subspace. I think that it isn't closed under addtion because sin90 +sin90 = 2 which isnt a solution to any elements of the set X. So i can use this as a counterexample right? I will start thinking about the other subsets.