 Hi and welcome to the session. Let us discuss the following question. Question says, find all points of discontinuity of f where f is defined by fx is equal to 2x plus 3 if x is less than equal to 2, fx is equal to 2x minus 3 if x is greater than 2. First of all, let us understand that function f is discontinuous at x is equal to a if f n side limit is not equal to right hand side limit of the function at x is equal to a. Now we can say limit of x tending to a plus fx is not equal to limit of x tending to a minus fx. This is the key idea to solve the given question. Let us now start the solution. We are given fx is equal to 2x plus 3 if x is less than equal to 2, fx is equal to 2x minus 3 if x is greater than 2. First of all, let us consider fx is equal to 2x plus 3 if x is less than 2. This is given in the question that fx is equal to 2x plus 3 if x is less than 2. Now clearly we can say this is a polynomial function and polynomial function is continuous at every real number. This implies function f is continuous at all real numbers less than 2. We are given fx is equal to 2x minus 3 if x is greater than 2 real function and below polynomial function is continuous at every real number. This implies that function f is continuous at every real number greater than 2. Let us now check the continuity of the function at x is equal to 2. Clearly we can see the function is defined at x is equal to 2. So we can write fx is equal to 2. Function f is defined. Let us now find out the limit of the function at x is equal to 2. First of all we will find left hand side limit of the function fx is equal to limit of x 2 minus 2x plus 3 is equal to 2 multiplied by 2 plus 3. On simplifying we get 7. So we can write limit of x tending to 2 minus fx is equal to 7. Let us now find out right hand side limit. Limit of x tending to 2 plus fx is equal to 2 multiplied by 2 minus 3. On simplifying we get 1. So we get limit of x tending to 2 plus fx is equal to 1. Here we can see left hand side limit is not equal to right hand side limit. So by key idea we get the function is discontinuous at x is equal to 2. So the given function f is discontinuous at x is equal to 2. This is our required answer. This completes the session. Hope you understood the session. Goodbye.