Consider $[\cdot]$ and ${\cdot}$ denote the greatest integer function and the fractional part function, respectively.
Let $f (x) = {x} + \sqrt{{x}}$ .
Statement I: f is not differentiable at integral values of x.
Statement II : f is not continuous at integral points

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

Statement II is correct but Statement I is incorrect

Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I

Statement I is correct but Statement II is incorrect

Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Question Image
The function is not differentiable and continuous at two points between $x = - π / 2$ and $x = π / 2$ . Also, the function is not continuous at $x = \frac{π}{2}$ and $x = - \frac{π}{2}$ . Hence, at four points, the function is not differentiable.