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Maths-

General

Easy

Question

For each x in [0, 1] define f(x) = $blank open curly brackets table row cell 2 x end cell cell comma text if end text 0 less or equal than x less or equal than fraction numerator 1 over denominator 2 end fraction end cell row cell 2 minus 2 x end cell cell comma text if end text fraction numerator 1 over denominator 2 end fraction less than x less or equal than 1 end cell end table close$ Let f^((b)(x)=f(f(x)), f^(n+(a)(x) = f⁽ⁿ⁾(f(x)) for each integer n 2. For how many values of x is [0, 1] is f⁽²⁰⁰⁸⁾ (x) = 1/2?

0
2008
2008²
2²⁰⁰⁸

The correct answer is: 2²⁰⁰⁸

Function is symmetrical about x = 1/2 f⁽ⁿ⁾(x) is symmetrical about x = $fraction numerator 1 over denominator 2 end fraction$

Number of solution of f(x) = 1/2 is 2
Number of solution of f(f(x) = 1/2 is 2²
Number of solution of f(f(f(x)) = 1/2 is 2³
Number of solution of f²⁰⁰⁸ (x) = $fraction numerator 1 over denominator 2 end fraction$ is 2²⁰⁰⁸ .

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