Suppose that $f$ has the property that $f(x+y)=f(x)+f(y)$.

Question

I am given the assumption that a function $f$ has the property that $f(x+y)=f(x)+f(y)$. I am wondering if it follows that $f(x-y)=f(x)-f(y)$. I think that this is false, yet I see this being used in proofs.

Answer 1

We have $f(x-y)+f(y)=f((x-y)+y)$.