 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says let f and g be two functions from r to r we define respectively by fx is equal to x plus 1 and gx is equal to 2x minus 3. Find f plus g, f minus g and f divided by g. So let us begin with the solution and here we are given two functions f from r to r which is defined by fx is equal to x plus 1 and a function g which is also from r to r and defined by gx is equal to 2x minus 3 and first we have to find f plus g. Now by the definition of addition of two real functions f plus g of x is equal to fx plus gx and fx is x plus 1 and gx is 2x minus 3 which on simplifying comes equal to 3x minus 2 and this is for all x belonging to r. Now applying the definition of the difference of two real functions to find the second part here we have to find f minus g again f minus g of x is equal to fx minus gx and fx is equal to the function x plus 1 minus and gx is the function 2x minus 3 which is equal to x plus 1 minus 2x plus 3 which is further equal to minus x plus 4 and this is also for all x belonging to r. Now let us find quotient of two real functions that is f upon g. f upon g of x is equal to fx upon gx and fx is a function which is defined by x plus 1 and gx is a function defined by 2x minus 3. Now this is a function if the denominator is not equal to 0 that is 2x minus 3 is not equal to 0 or x is not equal to 3 upon 2 and for all x belonging to r f upon g of x is equal to x plus 1 upon 2x minus 3 for all x belonging to r and x not equal to 3 upon 2 and that is the answers are first the sum of the two real functions that is f plus g of x is equal to 3x minus 2 and we have to find the difference of these two functions that is f minus g of x which is equal to minus x plus 4 and then the quotient of f and g of x is equal to x plus 1 upon 2x minus 3 or x not equal to 3 upon 2. So this completes the solution hope you enjoyed this session take care have a good day.