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JEE Main202227 Jun 2022Evening ShiftMathematicsFunctionsActual

Let S = 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 . Define f : S → S as f n = 2 n , if n = 1 , 2 , 3 , 4 , 5 2 n - 11 if n = 6 , 7 , 8 , 9 , 10 Let g : S ≥ S be a function such that fog n = n + 1 , if n is odd n - 1 , if n is even , then g 10 g 1 + g 2 + g 3 + g 4 + g 5 is equal to

Correct answer

0

Step-by-step solution

Given, f n = 2 n ,   if   n = 1 , 2 , 3 , 4 , 5 2 n - 11   if   n = 6 , 7 , 8 , 9 , 10 So, f 1 = 2 , f 2 = 4 , ..... f 5 = 10 And f 6 = 1 , f 7 = 3 , f 8 = 5 ...... f 10 = 9 f g n = n + 1 ; n ∈   odd   n - 1 ; n ∈   even   So, f g 10 = 9 ⇒ g 10 = 10 f g 1 = 2 ⇒ g 1 = 1 f g 2 = 1 ⇒ g 2 = 6 f g 3 = 4 ⇒ g 3 = 2 f g 4 = 3 ⇒ g 4 = 7 f g 5 = 6 ⇒ g 5 = 3 So, g 10 · g 1 + g 2 + g 3 + g 4 + g 5 = 10 · 1 + 6 + 2 + 7 + 3 = 190

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