 Welcome to the session. I am Shashi and I am going to help you with the following question. Question says show that the function defined by fx is equal to cos x square is a continuous function. Now let us start the solution. You know function f is given by fx equal to cos x square. You know cosine function is defined at every real number. So we can write function f is defined at every real number. That function h is given by hx equal to x square and function g is given by gx equal to cos x. First of all let us consider function h given by hx equal to x square. This is a polynomial function and we know polynomial function is continuous at every real number. So function h is continuous at every real number. Let us consider function g given by gx equal to cos x. Now we know cosine function is continuous at every real number. So we can write function g is continuous at every real number. Let us find out composition of g and h that is g hx. This is equal to g hx. Now we know hx is equal to x square. So substituting for hx we get gx square. Now we know gx is equal to cos x. So gx square is equal to cos x square. Now this is equal to fx. Now clearly we can see function f is a composition of two continuous functions g and h. So we can write function f being a composition of two continuous functions is continuous. Here we have used the theorem if function g is continuous at c and if function f is continuous at gc then f of g is continuous at c. So our required answer is function f is continuous at every real number. So that is proved. This completes the session. Hope you understood the session. Take care and have a nice day.