 Hello and welcome to the session. Let's discuss the following problem today. Let every function defined from R to R be defined as fx is equal to 3x. Choose the correct answer A, f is 11 on 2, B, f is many 1 on 2, C, f is 11 but not on 2, D, f is neither 11 nor on 2. Now let us write the solution. Now let us first check for 11. Let x1, x2 belongs to R such that f of x1 is equal to f of x2 which implies 3x1 is equal to 3x2 which implies x1 is equal to x2. Therefore f from R to R is 11. Now let us check for on 2. Let y be any real number in R of codomain then fx is equal to y which implies 3x is equal to y which implies x is equal to y by 3. Now y by 3 belongs to R for y belongs to R such that f of y by 3 is equal to 3 into y by 3 which is equal to y. Thus for each y belongs to R of codomain there exists x is equal to y by 2 belongs to R of domain such that fx is equal to y thus f is on 2. Now f is 11 and f is on 2. Therefore f is a bijective function. Therefore the correct option is a which says that f is 11 on 2. Hence a is the correct answer. I hope you understood this problem. Bye and have a nice day.