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Let f : R → R be a function defined as f x = 6 i f x ≤ 1 a + b x i f 1 < x < 3 b + 5 x i f 3 ≤ x < 5 15 i f x ≥ 5 . Then, f is

Options

  1. Acontinuous in R if a = - 5 and b = 10
  2. Bcontinuous in R if a = 5 and b = 5
  3. Ccontinuous in R if a = 0 and b = 5
  4. Dnot continuous in R for any values of a and b

Correct answer

D. not continuous in R for any values of a and b

Step-by-step solution

Given, f x = 6 i f x &#8804; 1 a + b x i f 1 &#60; x &#60; 3 b + 5 x i f 3 &#8804; x &#60; 5 15 i f x &#8805; 5 Now, f 1 = 6 , f 1 - = 6 , f 1 + = a + b &#8230; . . i Also, f 3 = b + 15 , f 3 - = a + 3 b , f 3 + = b + 15 &#8230; . . i i Also, f 5 = 15 , f 5 - = b + 25 , f 5 + = 15 &#8230; &#8230; . i i i From i , i i and i i i , clearly, f is not continuous for any values of a and b .

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