 Hello and welcome to the session, let us discuss the following problem today. Let every function from r to r be defined as fx is equal to 10x plus 7, find the function from g to r to r such that dof is equal to f of g is equal to identity mapping from r to r. Now let us write the solution. Let every function from x to y, where x and y are proper subsets of r, consider an arbitrary element y and y, then y is equal to 10x plus 7, for some h belongs to x which implies x is equal to y minus 7 by 10. Now we define the function g from y to x such that g of y is equal to y minus 7 by 10. Now we have defined the function g of y, now let us find out g of f of x and f of g of y for this function. g of f of x which is equal to g of f of x which is equal to f of x minus 7 by 10 which is equal to 10x plus 7 minus 7 by 10 which is equal to x. Now let us find f of g of y which is equal to f of g of y which is equal to 10 into g of y plus 7 which is equal to 10 into y minus 7 by 10 plus 7 which is equal to y. Thus g of f of x is equal to identity mapping from r to r and f of g of y is also equal to identity mapping from r to r. Hence g of f is equal to f of g is equal to identity mapping from r to r. Thus we have proved that g of f is equal to f of g is equal to identity mapping from r to r. So the required function is g of y is equal to y minus 7 by 10. Therefore the required function for which g of f is equal to f of g is equal to identity mapping from r to r is g of y is equal to y minus 7 by 10. So this is the problem. Bye and have a nice day.