The function is $G(x,y)= 1$ if $y \neq e^{x}$ and $0$ if $y= e^{x}$.
2026-03-26 04:48:25.1774500505
Is this function continuous and differentiable?
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It is not continuous in the natural topology of $\mathbb{R}^2$, because a continuous function cannot assume exactly two values.
Therefore it is not differentiable, either.