The number of points where the function f x = 2 x 2 - 3 x - 7 if x ⩽ - 1 4 x 2 - 1 if - 1 < x < 1 x + 1 + x - 2 if x ⩾ 1 , where t denotes the greatest integer ⩽ t , is discontinuous is ______

Step-by-step solution

Here both the modulus function is continuous in its domain. At x = - 1 , lim x → - 1 - 2 x 2 - 3 x - 7 = 2   &   lim x → - 1 + 4 x 2 - 1 = 2 Hence f x is continuous at x = - 1 At x = 1 . lim x → 1 - 4 x 2 - 1 = 2   &   lim x → 1 + x + 1 + x - 2 = 3 Hence, f x is discontinuous at x = 1 For x ∈ - 1 , 1 the function f x is discontinuous when 4 x 2 - 1 = 0 /   1 /   2 i.e when x ∈ ± 1 2 , ± 1 2 , ± 3 2