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JEE Main20244 Apr 2024Evening ShiftMathematicsFunctionsActual

Consider the function f: R R defined by f(x)= 2 x 1+9 x^2 . If the composition of f, (f f f f) _ 10 times (x)= 2¹⁰ x 1+9 x^2 , then the value of 3 +1 is equal to ______

Correct answer

0

Step-by-step solution

aligned & f(f(x))= 2 f(x) 1+9 f^2(x) = 4 x 1+9 x^2+9.2^2 x^2 & f(f(f(x)))= 2^3 x / 1+9 x^2 1+9 (1+2^2 ) 2^2 x^2 1+9 x^2 = 2^3 x 1+9 x^2 (1+2^2+2^4 ) aligned By observation aligned & =1+2^2+2^4+ .+2¹⁸=1 ( (2^2 )¹⁰-1 2^2-1 )= 2²⁰-1 3 & 3 +1=2²⁰ 3 +1 =2¹⁰=1024 aligned

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