- #1
karnten07
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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 [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
Homework Equations
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 isn't 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.