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Let $y=\lfloor x \rfloor$, where $\lfloor x \rfloor$ is greatest integer less than or equal to $x$. Then

1. $y$ is continuous and many-one
2. $y$ is not differentiable and many-one
3. $y$ is not differentiable
4. $y$ is differentiable and many-one

The graph is discontinuos, so non-differentialble, and for two real numbers, a common image is there…

so Option B