I have been asking people and have been getting mixed answers. some people think it is the same because when you simplify the first one you get y=1, but some people think that they are different because in the first equation x cannot be 0, and in the second equation x can be 0. Please tell me.
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1$x/x$ is not defined for $x=0$. – Hagen von Eitzen Apr 30 '19 at 13:33
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I knew that already it was in the description – Apr 30 '19 at 13:33
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An expression alone is not a function. A function needs to have a domain specified. On the domain $\Bbb R\setminus \{0\}$ (or any subset thereof), they are the same function. On the domain $\Bbb R$, $\frac xx$ is not a function.
Arthur
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It’s worth noting that the reason $\frac{x}{x}$ is not a function on $\mathbb{R}$ is that a function must be defined on all of its domain. – 雨が好きな人 Apr 30 '19 at 13:39
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so what you are saying is that this is not a function because not for a function y must be defined for all x??? – Apr 30 '19 at 13:59
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@datboi By definition, yes, functions must have a value for every point in its domain. – Arthur Apr 30 '19 at 14:07