Consider the function f: R → R defined by f(x)=(2 x)/(√(1+9 x²)). If the composition of f, (f° f° f°° f) 10 times (x)=(2¹⁰ x)/(√(1+9 α x²)), then the value of √(3 α+1) is equal to _ _ _ _.

Sets, Relations and Functions: JEE Main 2024 Mathematics question

JEE Main 2024 · 4 Apr, Evening shift · Q37

JEE Main 20244 Apr, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

Consider the function

f: \mathbb{R} \rightarrow \mathbb{R}

defined by

f(x)=\frac{2 x}{\sqrt{1+9 x^2}}

. If the composition of

f, \underbrace{(f \circ f \circ f \circ \cdots \circ f)}_{10 \text { times }}(x)=\frac{2^{10} x}{\sqrt{1+9 \alpha x^2}}

, then the value of

\sqrt{3 \alpha+1}

is equal to _______.

Your answerType your answer. Integers and decimals are accepted.