Doubtify – JEE Ki Taiyaari, Simple Bhasha Mein

❓Question The number of points of discontinuity of the function f ( x ) = [ x 2 2 ] − [ x ] , x ∈ [ 0 , 4 ] , where  [ ⋅ ] denotes the greatest integer function , is equal to ? 🖼️ Question Image ✍️ Short Solution For functions involving GIF (floor) , remember this golden rule: 👉 Discontinuity occurs when the expression inside [ ] crosses an integer. We’ll find all such points for each term , then combine carefully. 🔹 Step 1 — Discontinuity points of [ x 2 2 ] \left[\dfrac{x^2}{2}\right] This term jumps when: x 2 2 = k , k ∈ Z \frac{x^2}{2} = k, \quad k\in\mathbb{Z} Given x ∈ [ 0 , 4 ] x\in[0,4] : x 2 2 ∈ [ 0 , 8 ] \frac{x^2}{2}\in[0,8] So possible integers: k = 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 k=0,1,2,3,4,5,6,7,8 Corresponding x x x -values: x = 2 k​ Within [ 0 , 4 ] [0,4] , these are: 0 ,   2 ,   2 ,   6 ,   2 2 ,   10 ,   12 ,   14 ,   4 So 9 potential jump points from this term. 🔹 Step 2 — Discontinuity points o...