Odd function

An odd function $f$ satisfies both $f(x)+f(-x)=0$ and $-f(x)=f(-x)$ .

For instance, $f(x)=3$ does not satisfy either, as $3+3\neq 0$ and $-3\neq 3$ . However, $f(x)=x$ does, as $x+-x=0$ and $-x=-x$

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