a) The inverse function of a function f(x)= [42+8(x^2)] / [1+(x^2)] with real numbers as variables is well defined if the domain is restricted. When this inverse function is called g(x), find the range of the largest interval among the ranges of the domain of g(x).

b) Find g(1) and g(1) for the inverse function x=g(y) of y= f(x) = 6x + cosx