finding domain of a complex function

Intro

If in a problem you are required to find the domain of a function which is the sum of two or more functions then the domain of the combined function will be the union of domains of individual function.

Sample Problem

Solution

To begin with this question we find the domain of sin(x) and 1/(e^x-1) individually and then take there union to get the domain of combined function..

domain of sin(x) is all real numbers
domain of 1/(e^x-1) is R-{0}
so the domain of combined function is R-{0} i.e the range which satisfies the domain of both the functions.