Let f(x)= ⁻¹(1- x ) ⁻¹(1- x ) 2 x (1- x ) , then which of the following is/are correct? [Note: k denotes fractional part function of k .]

Step-by-step solution

f(x)= ⁻¹(1- x ) ⁻¹(1- x ) 2 x (1- x ) f (0⁺ )= _ x 0⁺ (1-h) ⁻¹(1-h) 2 h (1-h) = 2 2 _ h 0 ⁻¹(1-h) h Let ⁻¹(1-h)= 1-h= h=1- l= 2 2 1- = 2 _ x 0 1 2 1+ = 2 III aligned f (0⁻ ) & = _ h 0⁻ ⁻¹(1-(1-h)) ⁻¹(1-(1-h)) 2(1-h) (1-(1-h)) & = _ h 0⁻ ⁻¹ h ⁻¹ h 2 h = 2 2 aligned