Question

what is the domain of 1/(x+1) ?

Answer 1

That function is the ratio of two numbers. The ratio is defined always, unless the number on the bottom is zero. That is undefined and is not allowed in mathematics. Therefore, you will always get an answer from this function, unless the number on the bottom, x+1 is equal to zero. So, the domain, the set of values which x can take, is defined so long as x+1 is not equal to zero. x+1 equals zero only when x = -1. So the domain is every real number except the number -1.