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Is there an odd function $g$ on domain $\mathbb{R}$, where $g(0)$ isn't equal to $0$ ?

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    $\begingroup$ Odd function means $f(-x)=-f(x)\,$. For $x=0$ that means $f(0)=-f(0)\,$. $\endgroup$
    – dxiv
    Commented May 10, 2017 at 7:48
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    $\begingroup$ Convince yourself by substituting $x=0$ here. $\endgroup$
    – drhab
    Commented May 10, 2017 at 7:49
  • $\begingroup$ Answer: It would be odd... $\endgroup$
    – Jean Marie
    Commented May 10, 2017 at 7:56

2 Answers 2

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Hint. Note that if $g$ is odd and it is defined at $0$ then $g(0)=-g(-0)=-g(0)$.

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Any odd function on $\Bbb R$ is a symmetric curve about the origin...and if $g(0)$ is not equal to zero,then $0$ must have to two images..and that will contradict the statement of a function.....so answer is NOT.

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