Let f:R → R be a function defined by f(x) = (2(1 - (x²⁵)/2)(2 + x²⁵))^(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 _ _ _ _ _ _.

Sets, Relations and Functions: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Morning shift · Q38

JEE Main 202225 Jun, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let

f:R \to R

be a function defined by

f(x) = {\left( {2\left( {1 - {{{x^{25}}} \over 2}} \right)(2 + {x^{25}})} \right)^{{1 \over {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 ____________.

Your answerType your answer. Integers and decimals are accepted.