Celebrating year 2016!

Algebra Level 5

fn+1(x)=77+fn(x)\large f_{n+1}(x)=\sqrt{7-\sqrt{7+f_{n}(x)}} and f1(x)=77+x\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? f2016(x)=x\large f_{2016}(x)=x


Inspiration.

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