Let f x = 2 x 2 + 1 and g x = 2 x - 3 , x < 0 2 x + 3 , x ≥ 0 , where t is the greatest integer ≤ t . Then, in the open interval - 1 , 1 , the number of points where fog is discontinuous is equal to ______.

Step-by-step solution

Given, f x = 2 x 2 + 1 and g x = 2 x - 3 , x < 0 2 x + 3 , x ≥ 0 Now, f g x = 2 g 2 x + 1 = 2 2 x - 3 2 + 1 ; x < 0 2 2 x + 3 2 + 1 ; x ≥ 0 If x < 0 then - 1 < x < 0 ⇒ - 2 < x < 0 ⇒ - 5 < 2 x - 3 < - 3 ⇒ ⇒ 9 < 2 x - 3 2 < 25 ⇒ 18 < 2 2 x - 3 2 < 50 , So there will be 31 values where 2 2 x - 3 2 is integer, Similarly for 2 2 x + 3 2 there will be 31 , so total 62 points of discontinuity