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 &#8594; R be defined as f x = x + x , x + x , x + x , - 1 &#8804; x &#60; 1 1 &#8804; x &#60; 2 2 &#8804; x &#8804; 3 , Where t denotes the greatest integer less than or equal to t . Then, f is discontinuous at:

Quantrex Academy · Accepted Answer

Correct answer: D. Only three points

f x = x + x ; - 1 &#8804; x &#60; 1 x + x ; 1 &#8804; x &#60; 2 x + x ; 2 &#8804; x &#8804; 3 = - x - 1 ; - 1 &#8804; x &#60; 0 x + 0 ; 0 &#8804; x &#60; 1 2 x ; 1 &#8804; x &#60; 2 x + 2 ; 2 &#8804; x &#60; 3 6 ; x = 3 &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; At x = 0 , &#160; 1 , &#160; 2 , &#160; 3 f changes its definition. &#8756; At x = 0 &#160; LHL = - 1 , &#160; RHL = 0 &#8658; f is discontinuous at x = 0 x = 1 &#160; LHL = 1 , &#160; RHL = 2 &#8658; f is discontinuous at

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:

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Correct answer

Step-by-step solution

More from Continuity and Differentiability

Let f : - 1,3 &#8594; R be defined as f x = x + x , x + x , x + x , - 1 &#8804; x &#60; 1 1 &#8804; x &#60; 2 2 &#8804; x &#8804; 3 , Where t denotes the greatest integer less than or equal to t . Then, f is discontinuous at:

Options

Correct answer

Step-by-step solution

More from Continuity and Differentiability

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: