So I have the question Let F be a field and let L be the set of all polynomials f(x) element of F[X] satisfying the condition that deg(f) is even. Is L a subspace of F[X]?
I would say that L is not a subspace of F[X].
Taking the condition f(-a)=-f(a)
if we took f(x)=x^2 -2, which has an even degree, then
f(-a)=(-a)^2 -2 = a^2 -2 which does not equal -(x^2 -2)
Is my approach correct?