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Find the number of all onto functions .?
Find the number of all onto functions from the set {1, 2, 3, ... , n} to itself.
Please just don't give the answer. I want detailed explanation as to how the answer was arrived at.
2 Answers
- No MythologyLv 78 years agoFavorite Answer
Count them. If f is any such function, you can consider how many choices there are for f(1). There are n possible values of f(1). These leaves n - 1 possible values for f(2), n - 2 possible values for f(3), and so forth.
A function from {1, 2, ..., n} onto itself is a permutation. How many ways can you permute n distinct objects? (Here's a hint: think "factor...")
- duenwaldLv 44 years ago
g o h maps -a million/4 that's named composition. you are able to rewrite it like this: g(h(-a million/4)) Now paintings from the interior, so plug into the h function first. 2(-a million/4) - 3= -a million/2 - 3 = -7/2 Now plug that answer into the g-function g(-7/2) = (-7/2)^2 + 2(-7/2) + a million =40 9/4 - 14/2 + a million combine and simplify. wish this helps : )
