Consider the functions a(z) and B(x) = e +e- In this question, you may freely use the fact that 8 (x)- a (x) = 1. (i) %3D Verify that a'(r) = B(r) and B'(r) = a(r). The function a is invertible. Use the Inverse Function Theorem to compute the derivative (ii) of a Simplify as much as possible, using the fact that B2(x) – a (r) =1 to write your answer without any a's or B's. (iii) the derivative of a (this time without using the Inverse Function Theorem) and confirm that you get the same answer as part (ii). |The inverse of a can be explicitly computed to be a(x) = In(r+ v + 1). Compute %3D