The number of functions f, from the setA=left | vedclass

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Question

$\left( x ^{2}-10 x +9\right) \leq 0 \Rightarrow( x -1)( x -9) \leq 0$

$x \in[1,9] \Rightarrow A =\{1,2,3,4,5,6,7,8,9\}$

$f ( x ) \leq( x -3)^{2

Vedclass · Accepted Answer

$1440$

Vedclass · Answer

$\left( x ^{2}-10 x +9\right) \leq 0 \Rightarrow( x -1)( x -9) \leq 0$

$x \in[1,9] \Rightarrow A =\{1,2,3,4,5,6,7,8,9\}$

$f ( x ) \leq( x -3)^{2}+1$

$x =1: f (1) \leq 5 \Rightarrow 1^{2}, 2^{2}$

$x =2: f (2) \leq 2 \Rightarrow 1^{2}$

$x =3: f (3) \leq 1 \Rightarrow 1^{2}$

$x =4: f (4) \leq 2 \Rightarrow 1^{2}$

$x =5: f (5) \leq 5 \Rightarrow 1^{2}, 2^{2}$

$x =6: f (6) \leq 10 \Rightarrow 1^{2}, 2^{2}, 3^{2}$

$x =7: f (7) \leq 17 \Rightarrow 1^{2}, 2^{2}, 3^{2}, 4^{2}$

$x =8: f (8) \leq 26 \Rightarrow 1^{2}, 2^{2}, 3^{2}, 4^{2}, 5^{2}$

$x =9: f (9) \leq 37 \Rightarrow 1^{2}, 2^{2}, 3^{2}, 4^{2}, 5^{2}, 6^{2}$

Total number of such function

$=2(6 !)=2(720)=1440$

The number of functions $f$, from the set$A=\left\{x \in N: x^{2}-10 x+9 \leq 0\right\}$ to the set $B=\left\{n^{2}: n \in N\right\}$ such that $f(x) \leq(x-3)^{2}+1$, for every $x \in A$, is.

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