For each of the following functions:
a) state the range of the function
b) find the inverse of the function, and give its domain
c) sketch the function and its inverse on the same graph

i) f(x) = 1 + sin 2x -pi/4<_ x <_ pi/4

ii) f(x) = 1/2 tan (x-pi/2) 0<_ x <_ pi