1. Consider the functions defined by f(x)=2e^(x-1)+2

(a)Describe the full set of transformations, which when applied to the graph of y=e^x produces the graph of f.

(b)Find the coordinates of the points where the graph of f cuts the axes (x and y-intercepts). USE e^-1 = 0.3679.

(c) Find the rule for the inverse function f^-1(x).

(d) Write down the domain of f^-1.

(e) Sketch the graph of y=f(x) and y=f^-1(x) on the same set of axes on the graph given. (e^-1 = 0.3679) include asymptotes, x and y intercepts for both f(x) and f^-1(x).