subspace qustion-exam coming up help!!-i dont understand

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}**

Re: subspace qustion-exam coming up help!!-i dont understand

Do you not know how to determine if A is a subspace of vetore space B?

First A must be a subset of B.

Then it must be "closed under addition": if u and v are in A then so is u+ v.

And it must be "closed under scalar multiplication: if v is in A and a is a scalar then av is in A.