Consider the rational function g(t) = (t-1)/(t+3)

Question

What is the domain and range of g^-1?

Answer 1

The domain of g is all Reals except -3.

 

The inverse of g is (-1-3t)/(t-1) so its domain is all Reals except 1.

 

Since the inverse function is obtained by interchanging variables, therefore the range of g^-1 is the domain of g;

the range of g^-1 is all Reals except -3.