ISI2015-DCG-57

Question

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

• A. $y$ is continuous and many-one
• B. $y$ is not differentiable and many-one
• C. $y$ is not differentiable
• D. $y$ is differentiable and many-one

Answer 1

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

so Option B

Answer 2

we all know that greatest integer function can't be continuous and differentiable at integer value 

The greatest integer function rounds any number down to the nearest integer. For example, 6.3 would get rounded down to 6, and 7.9 would get rounded down to 7.