JEE Main 2022 Mathematics question

Let f, g : N − {1} be functions defined by , where is the maximum of the powers of those primes p such that pᵅ divides a, and g(a) = a + 1, for all a N − {1}. Then, the function f + g is

(1)one-one but not onto
(2)onto but not one-one
(3)both one-one and onto
(4)neither one-one nor ontoCorrect

Answer: (4)

Solution

Computing (f + g)(a): (f + g)(2) = 1 + 3 = 4, (f + g)(3) = 1 + 4 = 5, (f + g)(4) = 2 + 5 = 7, (f + g)(5) = 1 + 6 = 7. Since (f + g)(4) = (f + g)(5), the

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Question ID VK-034417