Let $f(x) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\sin (x - [x])}}{{x - [x]}},}&{x \in ( - 2, - 1)} \\ {\max \,\,\,\left\{ {2x,3\left[ {\left| x \right|} \right]} \right\},}&{\left| x \right| < 1} \\ {1,}&{{\text{other}}\,\,{\text{wise}}} \end{array}} \right.$ Where $[t]$ denotes greatest integer $ \leqslant t.$ If $m$ is the number of points where $f$ is not continuous and $n$ is the number of points where $f$ is not differentiable, then the ordered pair $(m,n)$ is

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Analyzing +4 | -1

Let

f(x) = \left\{ {\begin{array}{cccccccccccccccccccc} {\frac{{\sin (x - [x])}}{{x - [x]}},}&{x \in ( - 2, - 1)} \\ {\max \,\,\,\left\{ {2x,3\left[ {\left| x \right|} \right]} \right\},}&{\left| x \right| < 1} \\ {1,}&{{\text{other}}\,\,{\text{wise}}} \end{array}} \right.

Where

[t]

denotes greatest integer

\leqslant t.

m

is the number of points where

f

is not continuous and

n

is the number of points where

f

is not differentiable, then the ordered pair

(m,n)

View answer and explanation

Correct option: C

(2, 3)

Option C ((2, 3)) is correct because the function f(x) is discontinuous at two points and not differentiable at three points.