 Hello and welcome to the session. In this session where we discuss a question which says that if f and g are real functions defined by f of x is equal to x square minus 1 and g of x is equal to 2x plus 3, then find first part f of x plus g of minus 2 second part square root of f of 2 over g of 2 third part p of minus 3g the whole of 4. Now let us start with the solution. Here f of x and g of x is given to us. So given f of x is equal to x square minus 1 and g of x is equal to 2x plus 3. Now let us start with the first part. Now f of x is equal to x square minus 1 therefore f cube x will be equal to f of x whole cube which will be equal to x square minus 1 whole cube. Now f cube 3 will be equal to, now here replacing the number of x by 3 it will be 3 square minus 1 whole cube. So this implies f cube 3 is equal to 9 minus 1 whole cube which is equal to 8 cube which is equal to 512. Also is equal to 5 minus 2 it will be 2 into minus 2 plus 3 which is equal to minus 4 plus 3 which is equal to minus 1. Now we have to find f cube 3 plus g of minus 2 and this is g of minus 2 so this will be equal to 12 minus 1 which is equal to 511. Now let us start with the second part. In the second part we have to find square root of g of 2. Now we have f of x is equal to x square minus 1 therefore it will be equal to, now replacing the value of x by 2 it will be 2 square minus 1 which is equal to 4 minus 1 which is equal to 3. Also g of x is equal to 2x plus 3 therefore equal to, now replacing the value of x by 2 here it will be 2 into 2 plus 3 which is equal to 4 plus 3 which is equal to 7. Therefore square root of g of 2 will be equal to, now f of 2 is 3 and g of 2 is 7 so it will be equal to square root of 3 by 7. Now in the third part minus 3g the whole minus 3 into g of 4. Now again therefore f of 4 will be equal to 4 square minus 1 which is equal to 16 minus 1 which is equal to 15 and g of x is equal to 2x plus 3 therefore will be equal to 2 into 4 plus 3 which is equal to 8 plus 3. Which is equal to 11. Now f of 4 minus 3 into g of 4 will be equal to, now putting the values of f of 4 and g of 4 here it will be 2 into 15 minus 3 into 11 which is equal to 13 minus 33 which is equal to minus 3. So this is the solution of the given question and that's all for this session. Hope you have enjoyed this session.