1971 AHSME Problem 30

Given the linear fractional transformation of x into f_1(x)=\dfrac{2x-1}{x+1}. Define f_{n+1}(x)=f_1(f_n(x)) for n=1,2,3,\cdots. Assuming that f_{35}(x)=f_5(x), it follows that f_{28}(x) is equal to

\textbf{(A) }x\qquad \textbf{(B) }\frac{1}{x}\qquad \textbf{(C) }\frac{x-1}{x}\qquad \textbf{(D) }\frac{1}{1-x}\qquad \textbf{(E) }\text{None of these}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.