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Pleasesir help me to solve this question ...I m not able to solve it ...Please sir

Pleasesir help me to solve this question ...I m not able to solve it ...Please sir

Question Image
Grade:12

1 Answers

Abhishek Singh
104 Points
one month ago
clearly f:A → A ==> image of A is mapped to A.
 
Consider x in A , if f(x) = y, Then following 2 result can be seen
1) f(y) = f(f(x))= fof(x) = x 
​2) f(x) = f(f(y)) = fof(y) = y 
Thus If we choose any 2 number (repetition may occur) ==> their images will just swap 
==> This is equivalent to choosing pairs in  in set of 4 . Following case arise 
 
1) 2 Pairs each with distinct number ==> 4C2 ways = 6 
​2) 1 Pair of distinct and other 2 numbers mapped to them selves = 4c2 ways 
3) All numbers mapped to themselves(identity map) = 1 way 
Thus 13 such functions can be made
 
 

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