Question

Ques) f: A to A
A = {1,2,3,4}
No of function if [f(f(i))=1]​

Answer 1

Answer:

The questions states that f:A→A is a function which satisfies f(f(x))=x. We have to find the number of such functions with A={1,2,3,4}.

The given condition clearly states that the function is the inverse of itself. Since the set A was given to be so small, I first tried to think of some familiar functions that could fit. I came up with f(x)=x and f(x)=5−x. But the answer was nowhere near 2.

I think there has to be a general method to find the no. of functions that satisfy a given condition instead of hit and trial and counting on fingers. But I'm not able to figure out what it is.