# 250 Followers problem!

Algebra Level 2

$\begin{eqnarray} f_1 (x)&=&x\\ f_2 (x)&=&1-x\\ f_3 (x)&=&\frac{1}{x}\\ f_4 (x)&=&\frac{1}{1-x}\\ f_5 (x)&=&\frac{x}{x-1}\\ f_6 (x)&=&\frac{x-1}{x}\\ \end{eqnarray}$

If we know that $$f_6 (f_m(x))=f_4(x)$$ and $$f_n (f_4(x))=f_3(x)$$, find the minimum value of $$m+n$$.

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