If f (x)= ⁻¹ x, ~g (x)= e ^x and h (x)= g ( f (x)) , then h ^ (x) h (x) =

Step-by-step solution

aligned f (x) & = ⁻¹ x ~g (x) & = e ^x ~h (x) & = g ( f (x)) & = e ^ ⁻¹ x ~h ^ (x) & = e ^ ⁻¹ x -1 1-x^2 ~h ^ (x) h (x) & = e ^ ⁻¹ x -1 1-x^2 e ^ ⁻¹ x = -1 1-x^2 aligned