 and welcome to the session. My name is Shashi and I am going to help you with the common question. Question says find all points of discontinuity of f where f is defined by fx is equal to x plus 1 if x is greater than equal to 1, fx is equal to x square plus 1 if x is less than 1. Let us now start the solution. We are given fx is equal to x plus 1 if x is greater than equal to 1 and fx is equal to x square plus 1 if x is less than 1. Now we are given fx is equal to x plus 1 if x is greater than 1. This is a polynomial function and we know polynomial function is continuous at every real number. This implies function f is continuous at every real number greater than 1. We are also given that fx is equal to x square plus 1 if x is less than 1. This is again a polynomial function. So we know polynomial function is continuous at every real number. This implies function f is continuous at every real number less than 1. Now let us check the continuity of the function at x is equal is equal to 1, clearly we can see function is defined at x is equal to 1. Let us now find right inside limit of the function, it x is equal to 1. So, we can write limit of x tending to 1 plus f x, this is equal to limit of x tending to 1 plus x plus 1, this is equal to 1 plus 1, which is called that equal to 2. So, we get limit of x tending to 1 plus f x is equal to 2. Now, let us find out left inside limit of the function at x is equal to 1. So, we can write limit of x tending to 1 minus f x is equal to limit of x tending to 1 minus f x is equal to x square plus 1. Now, this is equal to 1 square plus 1, which is further equal to 2. So, we get limit of x tending to 1 minus f x is equal to 2. Now, clearly we can see right hand side limit and left hand side limit coincide each other. Now, let us find out value of the function at x is equal to 1, this is equal to 1 plus 1 equal to 2. So, we get right hand side limit of the function is equal to left hand side limit of the function is equal to value of the function at x is equal to 1. So, we can write limit of x tending to 1 plus f x is equal to limit of x tending to 1 minus f x is equal to 1 is equal to 2. This implies function f is continuous at x is equal to 1. So, we get function f is continuous at all the real values of x greater than 1 less than 1 and equal to 1. So, this implies function f is continuous at all real numbers there is no point of discontinuity. So, this is our required answer this completes the session. Hope you understood the session good bye.