 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says let F is equal to a set having ordered pills 1, 1, 2, 3, 0 minus 1 and minus 1, minus 3 be a function from Z to Z, defined by Fx is equal to AX plus B. First I mean teaches A and B determine A and B. This is now begin with the solution. Here we are given a function F from Z to Z. Order pill 1, 1 belong to function F. This implies F at 1 is equal to 1. Also 2, 3 belongs to F. This implies F at 2 is equal to 3. 0 minus 1 belongs to F. This implies F at 0 is equal to minus 1 and last minus 1 minus 3. Order pill also belongs to F. This implies F at minus 1 is equal to minus 3. Now Fx is a function which is defined by AX plus B. For X is equal to 1, F at 1 is equal to 1. This implies A into 1 plus B is equal to 1 which further implies A plus B is equal to 1. Let this be equation number 1. For X is equal to 2 we have the value of the function as 3. So this implies A into 2 plus B is equal to 3 which further implies 2A plus B is equal to 3. Let this be equation number 2 and here we are required to find the values of A and B. This is subtract equation 1 from equation number 2 which gives 2A plus B minus A plus B is equal to 3 minus 1 which further implies that 2A plus B minus A minus B is equal to 2 plus B cancels out with minus B and we have A is equal to 2. Now putting A is equal to 2 an equation number 2 we have 2 into 2 plus B is equal to 3 which implies 4 plus B is equal to 3 or B is equal to 3 minus 4 which is equal to minus 1 and thus B is equal to minus 1. Hence the values of A and B are 2 and minus 1. So this completes the solution. Hope you enjoyed it. Take care and have a good day.