Let f(x)=tanx on the open interval (−2π,2π), and let g=f−1.
(a) Explain why f is invertible on the given interval and state the domain and range of g.
(b) Using analytic methods, derive a formula for g′(x) expressed entirely in terms of x.
(c) Evaluate g′(1), giving your answer correct to three decimal places.
(d) The point (1,g(1)) lies on the graph of g. Write the equation of the tangent line to the graph of g at that point.