 Hi and welcome to the session. Let us solve the following question together. It says find the range of each of the following functions. Now the function says 2-3x where x belongs to real number and is greater than 0 and the second function is x square plus 2 where x is a real number and the third function fx is equal to x where x is a real number. In this question we need to find the range for each of these sub parts one by one. So let us solve the question. Now in the first part we are given the function fx as 2-3x where x belongs to real number and is greater than 0 right. So for finding the range we have to find the values of fx for different values of x which belongs to the real number and is greater than 0. So we have fx is equal to 0. So that means 2-3x is equal to 0 that gives us the value of x as 2 by 3 right. Again if x is greater than 2 by 3 fx will always be negative right. So we conclude that fx can take all the real values between minus infinity to 2. Now why 2 is written over here? It's because we have taken the negative aspect of it but if we take the positive aspect of it that will be x is less than equal to 2 by 3 then our fx will always be in positive term and will be less than 2 right. So that is why here we have taken it from minus infinity to 2 and our range will be minus infinity to 2 that is with the open intervals. So this completes the first part of the question. Proceeding on with the second part here we are given the function fx as x square plus 2 where x is a real number. Now as x belongs to real number therefore x square is always greater than equal to 0 isn't it? So we can conclude that our fx is greater than equal to 2. So hence the range will be it will be the closed interval from one end and an open interval from the other end right. And now here if x is a real number fx can take all the real values that is greater than equal to 2 and hence the range of the function is the set of all real numbers that is greater than 2 so it is including 2 in it but then the interval can go on to the infinity and hence it is an open interval from this side. So this becomes the answer of our second part. Proceeding on with the third part we are given the function fx is equal to x and where x belongs to real number. So therefore it is a very simple fx belongs to all the real values and hence our range will be all the real values that it can take. So this completes the question that was given to us. I hope you enjoyed the session and make use of the definition of the range that is known to you. Bye for now.