JEE Main 2022 Mathematics question
Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define f : as f(n) = 2n if n = 1, 2, 3, 4, 5 and f(n) = 2n − 11 if n = 6, 7, 8, 9, 10. Let g : be a function such that f∘g(n) = n + 1 if n is odd and f∘g(n) = n − 1 if n is even. Then g(10)(g(1) + g(2) + g(3) + g(4) + g(5)) is equal to .
Answer: 190
Solution
f(1..5) = 2, 4, 6, 8, 10 and f(6..10) = 1, 3, 5, 7, 9. From f(g(n)) = n + 1 (n odd) or n − 1 (n even): f(g(10)) = 9 gives g(10) = 10; f(g(1)) = 2 gives g(1) = 1;
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