If f(x)= array cl - ⁻¹ x x+1 , & x -1 1 , & x=-1 array . is right continuous at x=-1 , then =

Step-by-step solution

_ x -1 - ⁻¹ x x+1 = _ x -1 - 1 2 ⁻¹ x -1 1-x^2 1 2 x+1 aligned & = _ x -1 x+1 ⁻¹ x 1-x^2 & = _ x -1 1 ⁻¹ x 1-x = 1 1+1 & _ x -1 - ⁻¹ x x+1 = 1 2 aligned f(x) is right continuous on x=-1 aligned & _ x -1⁺ - ⁻¹ x x+1 =f(-1) & 1 2 = 1 =2 . aligned option (4) is correct.