Let f : 0 , 1 → ℝ be the function defined as f x = 4 x x - 1 4 2 x - 1 2 , where [ x ] denotes the greatest integer less than or equal to x . Then which of the following is(are) true?

Step-by-step solution

Given, f : ( 0 , 1 ) → ℝ f x = 4 x x - 1 4 2 x - 1 2 We know that, 4 x will be discontinuous function at integer points, So, critical point  = 1 4 , 1 2 , 3 4 as x ∈ 0 , 1 And function will be discontinuous at x = 3 4 because for 1 2   &   1 4 , x - 1 2   &   x - 1 4 2 will make the function continuos Hence, the function is discontinuous exactly at one point in 0 , 1 , so option A is correct, Now, f x = 0 ,   0 < x < 1 4 1 · x - 1 4 2 x - 1 2 , &#