 In this session, we are going to discuss the following question and the question says that Find the domain and range of the given rational function f of x is equal to x square minus 1 whole upon x minus 1. Let us start with the solution of the given question. In this question, we have to find the domain and range of the function f of x is equal to x square minus 1 whole upon x minus 1. First of all, we will find the domain. To find the domain of this function, we set the denominator equal to 0. So here, we set the denominator x minus 1 equal to 0 which implies that x is equal to 1. So we say that for x is equal to 1, the function becomes undefined hence this point should be excluded from the domain. So domain consists of all real numbers except 1 and we write domain is equal to the set of all x values where x belongs to the set of real numbers r and x is not equal to 1. It should be noted that while interpreting domain or range, we should not cancel out the common terms in the numerator and denominator. For other values, the function can be reduced as f of x is equal to x plus 1 the whole into x minus 1 the whole whole upon x minus 1. Here we have used the formula of a square minus b square which is equal to a plus b the whole into a minus b the whole and here in the numerator we have x square minus 1 which can be written as x square minus 1 square and using this formula this is equal to x plus 1 the whole into x minus 1 the whole and here if we cancel out the common terms that is x minus 1 cancels with x minus 1 and here we have f of x is equal to x plus 1. Now if we put the value of x as 1 then the given function will become f of x is equal to 1 plus 1 that is equal to 2 but x is equal to 1 is the excluded point in the domain. So f of x will never be equal to 2 or we can say that f of x will take all real values except 2 hence range of this function will be equal to the set of all f of x values such that f of x belongs to the set of real numbers are and f of x is not equal to 2 or we can also write it as the set of all y values such that y belongs to the set of real numbers are and y is not equal to 2. This is the required answer. This completes our session. Hope you enjoyed this session.