Let [x] denote the greatest integer function and \(f(x)=\max \{1+x+[x], 2+x, x+2[x]\}, 0 \leq x \leq 2\).
Let m be the number of points in [0,2], where f is not continuous and n be the number of points in (0,2), where f is not differentiable. Then \((m+n)^2+2\) is equal to

[JEE Main 2023, 15 Apr (Shift 1)]

Question

Let [x] denote the greatest integer function and \(f(x)=\max \{1+x+[x], 2+x, x+2[x]\}, 0 \leq x \leq 2\).
Let m be the number of points in [0,2], where f is not continuous and n be the number of points in (0,2), where f is not differentiable. Then \((m+n)^2+2\) is equal to

[JEE Main 2023, 15 Apr (Shift 1)]

YESPYQ · Accepted Answer

Options are free to see. Unlock the correct answer and full explanation with PYQ Pass.

Let [x] denote the greatest integer function and \(f(x)=\max \{1+x+[x], 2+x, x+2[x]\}, 0 \leq x \leq 2\). Let m be the n…

Practice more JEE Maths PYQs