Verified Solution • 2025–26 Session
moderate
QJEEM21Mac764: JEE Main 2021 Mathematics - Class 12 JEEM21Mac764 Solution: Let a function f : R R be defined as f ( x ) = { sin x − e x…
Let a function f : R R be defined as
where [ x ] is the greatest integer less than or equal to x. If f is continuous on R, then (a + b) is equal to:
where [ x ] is the greatest integer less than or equal to x. If f is continuous on R, then (a + b) is equal to:
Multiple Choice Options
- A 4
- B 3
- C 2
- D 5
Step-by-Step Verified Solution
Continuous x = 0
f(0+) = f(0 ) a 1 = 0 e0
a = 0
Continuous at x = 1
f(1+) = f(1 )
2(1) b = a + ( 1)
b = 2 a + 1 b = 3
a + b = 3
f(0+) = f(0 ) a 1 = 0 e0
a = 0
Continuous at x = 1
f(1+) = f(1 )
2(1) b = a + ( 1)
b = 2 a + 1 b = 3
a + b = 3