 Hello and welcome to the session. In this session we shall discuss radical functions and their domain. First of all we shall discuss radical functions. A radical function is a function that has a variable inside the root. Now this includes square roots, cube roots or any nth root. Now y is equal to nth root of x is a radical function where x is called radicand, n is called the index and this root sign is called radical sign. For example in y is equal to square root of x plus 2 the whole, radicand will be equal to x plus 2 and index will be equal to 2. We should note that it does not include functions that contain only numerous inside the radicals and independent variable must lie inside the radical. An example of non-radical function will be y is equal to x plus square root of 5. Here we should note that in this function we have only number inside the radical so it is a non-radical function. It is very easy to solve equations involving radicals and the steps involved in solving radical equations are as follows. The first step is to isolate the radical on one side of the equation. Then both sides of the equation are taken to the same power of the root. That is if there is cube root we take cube of both sides then remove the root and leave everything inside it as it is. Next solve the obtained equation using basic concepts of algebra and lastly check your answer. Let us take an example. Solve for x and the equation given is square root of x minus 2 the whole plus 4 is equal to 6. Now we are going to solve this radical equation using these steps. So in the first step we isolate the radical on one side of the equation. That is our equation is square root of x minus 2 the whole plus 4 is equal to 6 and we get square root of x minus 2 the whole is equal to 6 minus 4 which implies that square root of x minus 2 the whole is equal to 2. Here we have square root so in the second step we shall square both sides. On squaring both sides we get x minus 2 is equal to 2 square which implies that x minus 2 is equal to 4. Now in the next step we shall solve this equation. Now here adding 2 on both sides of the equation we get x minus 2 plus 2 is equal to 4 plus 2 which implies that x is equal to 6. Thus we have got the value of x as 6. Now in the last step we shall check our answer that is we put x is equal to 6 in the given radical equation that is square root of x minus 2 the whole plus 4 is equal to 6 and we get square root of 6 minus 2 the whole plus 4 is equal to 6 which implies that square root of 4 plus 4 is equal to 6 which further implies that 2 plus 4 is equal to 6 that is 6 is equal to 6 which is true so x is equal to 6 is the required solution. Now we are going to discuss domain of a radical function. We know that the domain of a function f of x is the set of all values of x for which the function f of x is defined. Now to find domain of radical functions follow these steps. Here first of all we determine the index then we check that if index is an odd number then domain is set of real numbers and if index is an even number then we must restrict the domain to make radicand greater than equal to 0 that is we set the expression inside the radical greater than or equal to 0. Let us consider an example. Find the domain of the functions f of x is equal to square root of x minus 4 and f of x is equal to cube root of x. Here in the first part we have the function f of x is equal to square root of x minus 4 since it is a square root function so we can say that index here is equal to 2 which is even. So here we must restrict the domain to make radicand greater than equal to 0. Here radicand is equal to x minus 4. So restricting the domain we have x minus 4 is greater than equal to 0. Now adding 4 on both sides we get x minus 4 plus 4 is greater than equal to 0 plus 4 which implies that x is greater than equal to 4 so in such notation domain of the function f of x will be equal to the set of all x such that x is greater than equal to 4 where x belongs to the set of real numbers. In interval notation domain of the function f of x is equal to semi-closed interval from 4 to infinity. In the second part the function f of x is equal to cube root of x. Here we can say that index is equal to 3 and radicand is equal to x. Now index is equal to 3 which is odd. So domain is set of all real numbers in set notation domain of the function f of x is equal to the set of all x such that x belongs to the set of real numbers and in interval notation domain of the function f of x is equal to the open interval minus infinity to infinity. Thus in this session we have discussed radical functions and their domain. This completes our session. Hope you enjoyed this session.