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

JEE Main 2022 Mathematics question

The number of functions f, from the set A = {x N : 0} to the set : n N} such that , for every x A, is .

Answer: 1440

Solution

A = {1, 2, …, 9} and B = {1, 4, 9, 16, …}. The condition gives the bounds 5, 2, 1, 2, 5, 10, 17, 26, 37 for x = 1, …, 9. The number of perfect squares allowed is 2 (1, 4), 1,

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Question ID VK-034347