QJEEM21Macbea: JEE Main 2021 Mathematics - Class 12 JEEM21Macbea Solution: Let [t] denote the greatest integer less than or equal to t.…
Let [t] denote the greatest integer less than or equal to t. Let f(x) = x − [x], g(x) = 1 − x + [x], and h(x) = min{f(x), g(x)}, x ∈ [−2, 2]. Then h is :
Multiple Choice Options
Acontinuous in [ − 2, 2] but not differentiable at more than four points in ( − 2, 2)
Bnot continuous at exactly three points in [ − 2, 2]
Ccontinuous in [ − 2, 2] but not differentiable at exactly three points in ( − 2, 2)
Dnot continuous at exactly four points in [ − 2, 2]
Step-by-Step Verified Solution
min{x − [x], 1 − x + [x]}
h(x) = min{x − [x], 1 − [x − [x])}
⇒ always continuous in [−2, 2] but not differentiable at 7 points.
