Question

In the following [x] denotes the greatest integer less than or equal to x.
Match the functions in Column I with the properties in Column II and indicate your answer by darkening the appropriate
bubbles in the 4x4 matrix given in the ORS.

Answer 1

(A). $x|x|$ is continuous, differentiable and strictly increasing in $(-1,1)$ .
(B). $\sqrt{{|}_X|}$ is continuous in $(-1,1)$ and not differentiable at $x=0$.
(C).
$x+\left[x\right]$ is strictly increasing in $(-1,1)$ and
discontinuous at $x=0\Rightarrow$ not differentiable at
$x=0$.
(D). $|x-1|+|x+1|=2$ in $(-1,1)$
$\Rightarrow$ the function is continuous and differentiable in $(-1,1)$ .