Let f : - 1,3 → R be defined as f x = x + x , x + x , x + x , - 1 ≤ x 1 1 ≤ x 2 2 ≤ x ≤ 3 , Where t denotes the greatest integer less than or equal to t . Then, f is discontinuous at:

Question

Let f : - 1,3 → R be defined as f x = x + x , x + x , x + x , - 1 ≤ x 1 1 ≤ x 2 2 ≤ x ≤ 3 , Where t denotes the greatest integer less than or equal to t . Then, f is discontinuous at:, Only one point, Only two points, Four or more points, Only three points

MARKS App · Accepted Answer

f x = x + x ; - 1 ≤ x 1 x + x ; 1 ≤ x 2 x + x ; 2 ≤ x ≤ 3 = - x - 1 ; - 1 ≤ x 0 x + 0 ; 0 ≤ x 1 2 x ; 1 ≤ x 2 x + 2 ; 2 ≤ x 3 6 ; x = 3 At x = 0 , 1 , 2 , 3 f changes its definition. ∴ At x = 0 LHL = - 1 , RHL = 0 ⇒ f is discontinuous at x = 0 x = 1 LHL = 1 , RHL = 2 ⇒ f is discontinuous at x = 1 x = 2 LHL = RHL = f 2 = 4 ⇒ f is continuous at x = 2 x = 3 LHL = 5 , f 3 = 6 ⇒ f is discontinuous at x = 1 ∴ Points of discontinuity are 0 , 1 , 3 .

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