Hello,

I would really appreciate it if someone could help me with these questions .

thanks

Determine whether or not Q is a subspace of F.

Let Q ={f which is an element of F such that df(x)/dx=2f(x)

Also,Determine whether or not P is a subspace of F.

LetP={f which is an element of F such that df(x)/dx=2x}

also how do I approach these questions? which ones are vector spaces of F and why?

F = { f :R−→R | f a function } is a vector space.

S1 = {f : R → R | f(x) = f(−x) for all x ∈ R}

S2 = {f : R → R | f(−2) = 0}

S3 = {f : R → R | f(x) = −2 for all x ∈ R}