 Hello and welcome to the session. Let us discuss the following problem today. If fx is equal to 4x plus 3 upon 6x minus 4, x not equal to 2 upon 3. Show that f for fx is equal to x for all x not equal to 2 upon 3. What is the inverse of f? Let us start with the solution now. We are given fx is equal to 4x plus 3 upon 6x minus 4. We have to find f for fx. We know f for fx is equal to f of fx. Now we will substitute for fx and get f 4x plus 3 upon 6x minus 4. Now this is quarter equal to 4 multiplied by 4x plus 3 upon 6x minus 4 plus 3 upon 6 multiplied by 4x plus 3 upon 6x minus 4 On simplifying we get 16x plus 12 plus 18x minus 12 upon 24x plus 18 minus 24x plus 16 plus 12 and minus 12 get cancelled Last 24x and minus 24x get cancelled and we get 34x upon 34. This is further equal to x. I have 34 and 34 will get cancelled and we get f for fx equal to x. Every x not equal to 2 upon 3. Now let us understand how do we find the inverse? Let us consider a function f from x to y and g is any function from y to x. If g of f is an identity function on x and f for g is an identity function on y then g is inverse of f. We have to find the inverse of f itself and f for fx is equal to x that is the identity function on x. So the inverse of f is f itself. So we can write inverse of f is because f for fx is equal to identity function on x. So this is our required answer. This completes the session. Hope you understood the session. Goodbye.