Celebrating year 2016!

Algebra Level 5

\(\large f_{n+1}(x)=\sqrt{7-\sqrt{7+f_{n}(x)}}\) and \(\large f_{1}(x)=\sqrt{7-\sqrt{7+x}}\)

A sequence of functions is defined by the previous recursive definition. Which one of the options is true for the following equation? \[\large f_{2016}(x)=x\]


Inspiration.

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