1971 AHSME Problems/Problem 30

Problem

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

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

Solution 1

$\boxed{\textbf{(D) }\frac{1}{1-x}}$ .

Solution 2

$\boxed{\textbf{(D) }\frac{1}{1-x}}$ .

1971 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 29	Followed by Problem 31
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35
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1971 AHSME Problems/Problem 30

Contents

Problem

Solution 1

Solution 2

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