JEE Main202227 Jul 2022Morning ShiftMathematicsFunctionsActual
Let f , g : ℕ - 1 → ℕ be functions defined by f a = α , where α is the maximum of the powers of those primes p such that p α divides a , and g a = a + 1 , for all a ∈ ℕ - 1 . Then, the function f + g is
Options
- Aone-one but not onto
- Bonto but not one-one
- Cboth one-one and onto
- Dneither one-one nor onto
Correct answer
D. neither one-one nor onto
Step-by-step solution
Given, f , g : N - 1 → N defined as f a = α , where α is the maximum power of those primes p such that p α divides a. g a = a + 1 Now, f 2 = 1 ,    g 2 = 3    ⇒    f + g 2 = 4 f 3 = 1 ,    g 3 = 4   ⇒   f + g 3 = 5 f 4 = 2 ,    g 4 = 5   ⇒   f + g 4 = 7 f 5 = 1 ,    g 5 = 6    ⇒   f + g 5 = 7 We can see f + g 5 = f + g 4 , so f + g is not one-one function Now, again we can see