An algebra problem by Harshit Mittal

Algebra Level 3

Let f ( x ) f(x) = x + 1 x − 1 \frac{x+1}{x-1}
Then f ( f ( f ( f ( f ( f ( f ( . . . . . . . . f ( f ( 2016 ) ) ) ) ) ) ) ) ) ) ) ) ) . . . ) ) ) ) ) ) f(f(f(f(f(f(f(........f(f(2016)))))))))))))...)))))) = ?
There are even number of f ( x ) f(x)

126 0 1008 63 1 504 2016 252

Harshit Mittal by Harshit Mittal , 23, India

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1 solution

Harshit Mittal
Mar 7, 2016

As it is in Componendo - Dividendo form we can take x 1 \frac{x}{1}
Then substitute x = 2016.
f ( 2016 ) f(2016) = 2016

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