 Hello and welcome to the session. Let us discuss the following problem today. Give examples of two functions f from n to n and g from n to n sub that g of f is on 2 but f is not on 2. Let us write the solution. Let us consider f of x is equal to x plus 1 and g of x is equal to x minus 1 if x is greater than 1 and 1 if x is equal to 1. First we have to prove that f is not on 2. For this let f of x is equal to y then y is equal to x plus 1 which implies x is equal to y minus 1. Now if y is equal to 1 we have x is equal to 1 minus 1 which is equal to 0 but 0 is not a natural number therefore f is not on 2. Now let us consider g of f of x for x greater than 1 g of f of x is equal to g of f of x which is equal to g of x plus 1 which is equal to x plus 1 minus 1 which is equal to x thus g of f of x is equal to x therefore g of f is an identity function. I hope you understood this problem. Bye and have a nice day.