1967 AHSME Problems/Problem 14

Problem

Let $f(t)=\frac{t}{1-t}$ , $t \not= 1$ . If $y=f(x)$ , then $x$ can be expressed as

$\textbf{(A)}\ f\left(\frac{1}{y}\right)\qquad \textbf{(B)}\ -f(y)\qquad \textbf{(C)}\ -f(-y)\qquad \textbf{(D)}\ f(-y)\qquad \textbf{(E)}\ f(y)$

Since we know that $y=f(x)$ , we can solve for $y$ in terms of $x$ . This gives us

/[y=\frac{1}{1-x}\RightArrow y(1-x)=1 \RightArrow y-yx=1\RightArrow yx=y-1\RightArrow x=\frac{y-1}{y}[/

1967 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 13	Followed by Problem 15
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