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## Homework Statement

Consider w= {f [itex]\in[/itex] F([itex]\Re[/itex]|f(-x)=f(x) for all x [itex]\in[/itex]R

Use the subspace test to verify W is a subspace of F(R)

## Homework Equations

## The Attempt at a Solution

0 is in W obviously

for closure under addition:

(f+g)(x) = (f+g)(-x) = f(x) +g(x) = f(-x)+g(-x)

I am confused how to verify closure under scalar multiplication

af(x) = af(-x) = (af)(x)=(af)(-x)?

I am not sure how to do this please help thanks