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Are they the same function?

$$y=\frac{x^2}{x}$$ and $$y=x$$

For the first function, if we don't divide both the numerator and the denominator by x, then the domain of it is the real line except the point x = 0, which is different from the domain of the second function.

Mikasa
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GoCurry
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    These are not technically the same, as you have noted. One has a removable singularity at $0$, the other does not, but otherwise they take the same values everywhere. – Valborg Sep 26 '16 at 17:46
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    These functions have different domains, so they are technically different functions. It is common, however, to disregard this when it is convenient to do so. – Ben Grossmann Sep 26 '16 at 17:46

1 Answers1

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The are not the same function, since they have different domains. For two function to be the same they should have the same domain and the same mapping rules.

Matata
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