Question

if the function f : A -> A , A={1,2,3,4} then find the total number of onto function

Answer 1

As the mapping is on the same function, the first element of the function can be mapped to any of the elements on the second function where in this case is the same function. The secomd element can be mapped to any of the elements except the element which is already mapped by the first element and so on.
Therefore the total number of onto functions is m!. ie 4!=24 onto functions.