The number of points of discontinuity of the function , where denotes the greatest integer function, is __________. [2025]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
The number of points of discontinuity of the function $f (x)$ $= [\frac{x^{2}}{2}] - [\sqrt{x}], x \in [0, 4]$ , where $[\cdot]$ denotes the greatest integer function, is __________. [2025]

Ans.
(8)

Values of x, where $[\frac{x^{2}}{2}]$ may be discontinuous on $x \in [0, 4]$ are $\sqrt{2}, 2, \sqrt{6}, 2 \sqrt{2}, \sqrt{10}, 2 \sqrt{3}, \sqrt{14}, 4$

And for $[\sqrt{x}]$ , values of x are = 1, 4

On checking for continuity at these points, we get f(x) is discontinuous at $x = 1, \sqrt{2}, 2, \sqrt{6}, 2 \sqrt{2}, \sqrt{10}, 2 \sqrt{3}, \sqrt{14}$ and continuous at x = 4.

Hence, f(x) is discontinuous for 8 values of $x \in [0, 4]$ .

Want Us to Email you About Special Offers & Updates?