The number of functions f, from the set 
to the set
such that 
, for every x 
A, is_________.
Text Solution
Verified by Experts1440
(1440)
(x 2 - 10x + 9) 
0 
(x - 1) (x - 9) 
0
x 
[1, 9] 
A = (1, 2, 3, 4, 5, 6, 7, 8, 9}
f(x) 
(x - 3) 2 + 1
x= 1 : f(1) 
5 
1 2 , 2 2
x = 2 : f(2) 
2 
1 2
x = 3 : f(3) 
1 
1 2
x = 4 : f(4) 
2 
1 2
x = 5 :f(5) 
5 
1 2 , 2 2
x = 6:f(6) 
10 
1 2 , 2 2 , 3 2
x = 7:f(7) 
17 
1 2 ,2 2 , 3 2 ,4 2
x = 8 : f(8) 
26 
1 2 , 2 2 , 3 2 , 4 2 , 5 2
x = 9 : f(9) 
37 
1 2 , 2 2 , 3 2 , 4 2 , 5 2 , 6 2
Total number of such function
= 2(6!) = 2(720) = 1440
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