(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

V is the set of functions R -> R; pointwise addition and (a.f)(x) = f(ax) for all x.

is V a vector space given the operations?

2. Relevant equations

nil.

3. The attempt at a solution

i think it is not closed under multiplication.

if r is an element of R, then

r*a(x) . r*f(x) = (r^2)*(a.f)(x)

which is not equal to

r*f(ax)

im not really sure if i even have the correct approach.

any help would be greatly appreciated.

thanks!

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# Vector spaces of functions

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