If f : [ 0 , 2 ) → ℝ is defined by f x = 1 + 2 x k  for  0 ≤ x < 1 k x  for  1 ≤ x < 2 , where k > 0 and f is such that lim x → 1 - f x = lim x → 1 + f x , then the value of k 2 is

Question

If f : [ 0 , 2 ) &#8594; &#8477; is defined by f x = 1 + 2 x k &#160;for&#160; 0 &#8804; x &#60; 1 k x &#160;for&#160; 1 &#8804; x &#60; 2 , where k &#62; 0 and f is such that lim x &#8594; 1 - f x = lim x &#8594; 1 + f x , then the value of k 2 is

Aicharya · Accepted Answer

Given: f x = 1 + 2 x k &#160;for&#160; 0 &#8804; x &#60; 1 k x &#160;for&#160; 1 &#8804; x &#60; 2 Now, lim x &#8594; 1 - f x = lim x &#8594; 1 + f x &#8658; 1 + 2 k = k &#8658; k + 2 = k 2 &#8658; k 2 - k - 2 = 0 &#8658; k 2 - 2 k + k - 2 = 0 &#8658; k + 1 k - 2 = 0 &#8658; k = 2 &#160; and &#160; - 1 But, k &#62; 0 Hence, k = 2 &#8658; k 2 = 4 .

If f : [ 0 , 2 ) → ℝ is defined by f x = 1 + 2 x k  for  0 ≤ x < 1 k x &#160…

Solution

If f : [ 0 , 2 ) &#8594; &#8477; is defined by f x = 1 + 2 x k &#160;for&#160; 0 &#8804; x &#60; 1 k x &#160…

Solution

If f : [ 0 , 2 ) → ℝ is defined by f x = 1 + 2 x k for 0 ≤ x < 1 k x &#160…