 Hi and welcome to the session. My name is Shashi and I am going to help you with the following question. Question says, examine that sine modulus of x is our continuous function. Let us now start the solution. Function f is given by fx is equal to sine x. Function g is given by gx is equal to modulus of x. For let us consider fx is equal to sine x. This is a sine function and we know sine function is continuous at every real number. It implies function f is continuous at every real number. Let us consider the function gx equal to modulus of x for all real x. Modulus function and we know modulus function is continuous at every real number. It implies function g is continuous at every real number. Find out composite of f and g that is f o gx. We know f o gx is equal to f gx modulus of x. No, fx is equal to sine x. So, f of modulus of x is equal to sine modulus of x. Now we have seen that functions f and g are continuous for every x belonging to real number. Therefore, the composite function f o gx is equal to sine modulus of x is also continuous for all real values of x. So, we can write since f and g are continuous for every x belonging to real numbers. So, composite function f o gx is equal to sine modulus of x is also continuous for all real values of x. This is because we know that theorem f and g are real valued functions such that f o g is defined at c. Then if g is continuous at c and if f is continuous at gc, then f o g is continuous at c. Or we can say composite of continuous functions is also continuous. So, this is our required answer. This completes the session. Hope you understood the session. Good bye.