 Hello and welcome to the session. Let us understand the following problem today. Check the inactivity and subjectivity of the function. We have a given function f from z to z given by fx is equal to x cube. Now let us write the solution. Let us check for one month first. Let xy belongs to z such that f of x is equal to f of y which implies x cube is equal to y cube. Now on taking cube root it implies x is equal to y 1 1. Now let us check for on 2. We know set of integers z does not contain cube roots. y belongs to z in core domain then f of x is equal to y which implies x cube is equal to y which implies x is equal to y to the power 1 by 3 but for all y belongs to z in core domain y to the power 1 by 3 does not belongs to z in domain not on 2. Now we can see that f is 1 1 and f is not on 2 therefore the given function is injective but not surjective. I hope you understood the problem bye and have a nice day.