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## Homework Statement

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 R^R, f is differentiable and f'(0) = 0

V:= fR^R, f is polynomial of the form f=at^2 for some aR

= 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

## Homework Equations

## The Attempt at a Solution

U: i am not sure about 0 , is it differentiable if f=0

V,W: is that 0 belongs to the polynomial, in other words i am not sure about the definition of polynomial

X: 0 is an odd function ? I knew that odd+odd=odd function a*odd=odd function