In the expression (x+1)/(x-1), each x is replaced by (x+1)/(x-1). The resulting expression, evaluated for x=12, equals:

1958 AMC 12 Problem 4

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In the expression

\dfrac{x+1}{x-1},

each

x

is replaced by

\dfrac{x+1}{x-1}.

The resulting expression, evaluated for

x=\dfrac12,

equals:

3

-3

1

-1

none of these

Let

f(x)=\frac{x+1}{x-1}

and simplify

f(f(x))

Combine the numerator and denominator of the composed fraction separately

Let

f(x)=\frac{x+1}{x-1}.

Then

\begin{aligned} f(f(x)) &=\frac{\frac{x+1}{x-1}+1} {\frac{x+1}{x-1}-1}\\ &=\frac{\frac{2x}{x-1}}{\frac{2}{x-1}} =x. \end{aligned}

x=\frac{1}{2},

the value is

\frac{1}{2},

which is not listed.

Therefore, the correct answer is E.