Let f(t)=(t)/(1-t), t≠1. If y=f(x), then x can be expressed as:

1967 AMC 12 Problem 14

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14.

Let

f(t)=\dfrac{t}{1-t},

t\ne1.

y=f(x),

then

x

can be expressed as:

f\left(\dfrac1y\right)

-f(y)

-f(-y)

f(-y)

f(y)

Solve

y=\frac{x}{1-x}

for

x

Compare

\frac{y}{1+y}

with

f(-y)

From

y=\frac{x}{1-x}

we obtain

y-yx=x,

x=\frac{y}{1+y}.

Since

f(-y)=-\frac{y}{1+y},

this is

-f(-y).

Therefore, the correct answer is C.