 Hi and welcome to the session. My name is Shashi and I am going to help you with the following question. Question says, examine the continuity of the function fx is equal to 2x square minus 1 and x is equal to 3. First recall, let us understand that function is continuous at x is equal to a if function is defined at x is equal to a, we can say f a exists and then limit of x tending to a fx is equal to f a that is the value of the function equals the limit of the function and x is equal to a. This is the key idea to solve the dual question. Let us now start the solution. We are given fx is equal to 2x square minus 1. We can see this is a polynomial function. So, fx exists at x is equal to 3. So, now we will find limit of the function at x is equal to 3. So, we can write limit of x tending to 3 fx is equal to limit of x tending to 3 2x square minus 1. This is equal to 2 multiplied by 3 square minus 1 which is further equal to 18 minus 1 which is equal to 17. Therefore, we get limit of the function at x is equal to 3 as 17. Let us now find out the value of the function at x is equal to 3 that is f3 f3 is equal to 2 multiplied by 3 square minus 1 below fx is equal to 2x square minus 1. So, to find f3 we will substitute 3 for x. Now we get 2 multiplied by 9 minus 1 which is equal to 17. So, therefore f3 is equal to 17. Clearly we can see limit of the function is equal to 17 and value of the function is equal to 17 at x is equal to 3. So, we can write this implies limit of x tending to 3 fx is equal to f3 is equal to 17. So, we can write therefore function f is continuous at x is equal to 3. So, this is our required answer this completes our session hope you understood the solution goodbye.