Steps to solve domain and range of a function

Working Formula for finding Domain (D_f)

 

1. Solve y in terms of x. ( In some cases this step is not  required in case y is given in terms of x).

 

2. Find those values of x for which y is well-defined and real.

 

3. The set of the values of x for which y is well defined and real is domain of f. i.e. D_f

 

Working Formula for finding Range (R_f)

For Range we repeat steps 1 and 2 of Domain with the roles of x and y interchanged.

Thus if X= R, Y=R then Domain of f i.e., D_f = {x E R: f(x) E R} and R={f(x): x E D_f}