Continuity and Differentiability · Question 13

JEE Main 2026 (Online) 22nd January Evening ShiftMCQMedium📈 Topic in 35% papers+4−1

Let [ ] denote the greatest integer function, and let f(x) = \ 2x, x2 \. Let S = \x (-2, 2) : the function g(x) = |x| [x2 ] is discontinuous at x\. Then x S f(x) equals

2 - 2
2 6 - 3 2
1 - 2
6 - 2 2

Answer

(3) 1 - 2

Solution

For x (-2, 2): x2 [0, 4), so [x2] jumps where x2 = 1, 2, 3

x = 1, 2, 3

At these points |x| 0, so g(x) is discontinuous; at x = 0, g is continuous.

S = \ 1, 2, 3\

For x < 0: 2x < 0 < x2 f(x) = 2x

For x > 0: f(x) = x2 if x 2, f(x) = 2x if x 2

f(1) = 1, f( 2) = 2, f( 3) = 6

f(-1) = - 2, f(- 2) = -2, f(- 3) = - 6

f(x) = 1 + 2 + 6 - 2 - 2 - 6 = 1 - 2

Answer: (3)

JEE Main 2026 (Online) 22nd January Evening Shift

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