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JEE Main202225 Jun 2022Morning ShiftMathematicsFunctionsActual

Let f : R → R be a function defined by f x = 2 1 - x 25 2 2 + x 25 1 50 . If the function g x = f f f x + f f x , then the greatest integer less than or equal to g 1 is ______.

Correct answer

0

Step-by-step solution

Given f x = 2 1 - x 25 2 2 + x 25 1 50 f x = 2 - x 25 2 + x 25 1 50 = 4 - x 50 1 50 i.e. f f x = 4 - 4 - x 50 1 50 50 1 50 = x Now g x = f f f x + f f x = f x + x So g 1 = f 1 + 1 = 3 1 50 + 1 Hence g 1 = 3 1 50 + 1 = 2

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