Identity Function is Odd Function

Theorem

Let $I_\R: \R \to \R$ denote the identity function on $\R$.

Then $I_\R$ is an odd function.

Proof

\(\ds \map {I_\R} {-x}\)

\(=\)

\(\ds -x\)

Definition of Identity Function

\(\ds \)

\(=\)

\(\ds -\map {I_\R} x\)

Hence the result by definition of odd function.

$\blacksquare$