 Welcome to the session. Let us discuss the following question. Question says, show that the function defined by fx is equal to modulus of cos x is a continuous function. First of all, let us understand that if f and g are real valued functions such that f o g is defined at c. If g is continuous at c and if f is continuous at gc then f o g is continuous at c. This is the key idea to solve the given question. In short, we can explain this as composite of two continuous functions is always continuous. Let us now start the solution. Function g is given by gx is equal to cos x. Function h is given by hx is equal to modulus of x for all real x. Now we know gx is equal to cos x for all real x. This is a cosine function and we know cosine function is continuous at every real number. This implies function g is continuous at every real number, modulus of x for all real x. This is a modulus function and we know modulus function is continuous at every real number. This implies function h is continuous at every real number, modulus of cos x. Now find composite of function h and g. Now we will find out h o gx that is equal to h gx. Now gx is equal to cos x. So we can write h cos x which is further equal to modulus of cos x. You know hx is equal to modulus of x. So h cos x is equal to modulus of cos x. Now modulus of cos x is equal to fx. h and g are continuous functions at every real number. So their composite is also continuous at every real number. And we know their composite is equal to function f. So this implies function f is continuous at every real number. Required answer. This completes the session. Hope you enjoyed the session. Goodbye.