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JEE Main202227 Jul 2022Evening ShiftMathematicsFunctionsActual

The number of functions f , from the set A = x ∈ N : x 2 - 10 x + 9 ≤ 0 to the set B = n 2 : n ∈ N such that f x ≤ x - 3 2 + 1 , for every x ∈ A , is _______.

Correct answer

0

Step-by-step solution

For set A x 2 - 10 x + 9 ≤ 0 ⇒ x - 1 x - 9 ≤ 0 ⇒ x ∈ 1 , 9 i.e. A = 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 Given B = n 2 : n ∈ N Now f x ≤ x - 3 2 + 1 For x = 1 :   f 1 ≤ 5 ⇒ B ∈ 1 2 , 2 2 For x = 2 : f 2 ≤ 2 ⇒ B ∈ 1 2 For x = 3 : f 3 ≤ 1 ⇒ B ∈ 1 2 For x = 4 : f 4 ≤ 2 ⇒ B ∈ 1 2 For x = 5 : f 5 ≤ 5 ⇒ B ∈ 1 2 , 2 2 For x = 6 : f 6 ≤ 10 ⇒ B ∈ 1 2 , 2 2 , 3 2 For x = 7 :

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