 Hi, and welcome to the session. I am Shashri. Let us do one question. Question is, let function f from x to y be an invertible function. Show that the inverse of f inverse is f. That is f inverse whole inverse is equal to f. Let us start with the solution now. We know the given function f is from x to y is an invertible function. Now, since f is an invertible function, so we can say it is on 2 and 1 1 function or it is a bijective function. So, inverse of a bijective function is also a bijective. So, we can write since f is bijective, so f inverse is also bijective. Therefore, f inverse is a function from y to x is a bijective function. It is invertible. Now, since f inverse is bijective function, so inverse of f inverse is also bijective. So, we can write inverse of f inverse is a function from x to y is also bijective. x be an arbitrary element of x such that f x is equal to y for some y belonging to set y. f x is equal to y implies f inverse y is equal to x. We know f inverse is the inverse of f. f inverse y must be equal to x. Now, this order implies inverse of f inverse x must be equal to y. This is because we know inverse of f inverse is the inverse of f inverse. So, f inverse y is equal to x. Then, so inverse of f inverse x must be equal to y. Now, we know y is equal to f x. So, we can write inverse of f inverse x is equal to f x. Now, since x is an arbitrary element of set x, therefore, inverse of f inverse x is equal to f x for every x belonging to set x. Hence, we get inverse of f inverse is equal to f. This completes the session. Hope you enjoyed the session. Take care and goodbye.