 Hi and welcome to the session. My name is Shashi and I am going to help you with the following question. Question says, is the function defined by fx is equal to x plus 5 if x is less than equal to 1? fx is equal to x minus 5 if x is greater than 1? A continuous function. First of all let us understand that function f is continuous at x is equal to a if f a exists. Now we can say function is defined at x is equal to a. Then left hand side limit of the function is equal to right hand side limit of the function is equal to value of the function at x is equal to a. Which is the key idea to solve the given question? Let us now start the solution. We are given fx is equal to x plus 5 if x is less than equal to 1 and fx is equal to x minus 5 if x is greater than 1? First of all let us consider function given by fx is equal to x plus 5. This is a polynomial function and polynomial function is continuous at all real numbers. So this implies function f is continuous for all real values of x less than 1. Let us consider fx is equal to x minus 5. Now again this is a polynomial function and polynomial function is continuous at all real numbers. So this implies function f is continuous for all real values of x greater than 1. Now, let us take the continuity of the function at x is equal to 1, clearly we can see function is defined at x is equal to 1, so we can write at x is equal to 1 function f is defined. Now, let us find out left hand side limit of the function, so we can write limit of x tending to 1 minus f x is equal to limit of x tending to 1 minus x plus 5 which is equal to 1 plus 5 equal to 6, so we get left hand side limit of the function at x is equal to 1. Now, let us find out the right hand side limit 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 plus x minus 5. Now, this is equal to 1 minus 5 equal to minus 4, so we get right hand side limit of the function at x is equal to 1 as minus 4, clearly we can see left hand side limit of the function and the right hand side limit of the function at x is equal to 1 do not coincide, so we can write limit of x tending to 1 minus f x is not equal to limit of x tending to 1 plus f x. Now, this implies function f is not continuous at x is equal to 1, left hand side limit of the function is not equal to right hand side limit of the function, so function f is not continuous at x is equal to 1. This is our required answer, this completes the session, hope you understood the session, goodbye.