 Hi and welcome to the session, I am Asha and I am going to help you with the following question which says find the domain and range of the following real functions. Second is fx is equal to root over 9 minus x square. Let us now start with the solution and here we are given a real function fx is equal to root over 9 minus x square. What if fx is equal to y? So this implies y is equal to root over 9 minus x square. Now what is domain of f? Domain of f will be the set of values which x can take and range will be the set of values which y can take. Now fx is defined for all x 9 minus x square is greater than or equal to 0. That is x is less than or equal to 3 or greater than or equal to minus 3. Now let us draw the graph of y is equal to root over 9 minus x square to find the range of fx x dash this is y dash. Now graph of 9 minus x square when x is equal to 3 suppose this point denotes 3 then y is 0 this is the point which denotes 3 0 and when x is equal to minus 3 suppose this is the point which denotes minus 3 then again y is 0 and when x is equal to 0 0 lies in between this interval then y is equal to 3. So this is the point which denotes 0 3. So graph of this function will be a semicircle and now let us write the domain and range of f with the help of this graph. So domain of f will be the set of values which x can take and x is from minus 3 to plus 3 and thus we can say that domain of f is all those x such that x is less than or equal to 3 or greater than or equal to minus 3. Now let us write the range of f which will be the set of all those y such that y is from 0 and its maximum limit is up to 3 or we can also say that x such that 0 is less than or equal to x is less than or equal to 3. Yes this is the range and this is the domain. This completes the solution hope you enjoyed it take care and have a good day.