Find the difference.

Calculus Level pending

If f ( x ) = x − 1 2 \displaystyle f(x)=\frac{x-1}{2} then f ∘ ⋯ ∘ f ⏞ 2014 times = x − a b \overbrace{f \circ \dots \circ f}^{2014\:\text{times}}=\frac{x-a}{b}

Find b − a b-a .


The answer is 1.

Aditya Jain by Aditya Jain , 26, India

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1 solution

Mrinal Abrol
Apr 18, 2014

f(x) = (x-1)/2

fof(x) = (x-3)/2

fofof(x) = (x-7)/2

Therefore, following the trend

fofofofo............ n times = (x - (2ⁿ - 1))/2ⁿ

For n = 2014

b = 2^2014 a = 2^2014 - 1

Performing b-a

We get b-a =1

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