If x=1+2^p and y=1+2^-p, then y in terms of x is:

1970 AMC 12 Problem 3

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x=1+2^p

and

y=1+2^{-p},

then

y

in terms of

x

is:

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

\dfrac{x+2}{x-1}

\dfrac{x}{x-1}

2-x

\dfrac{x-1}{x}

Solve the first equation for

2^p

Use

2^{-p}=\frac{1}{2^p}

and simplify

1+\frac{1}{x-1}

From

x=1+2^p

we get

2^p=x-1,

\begin{aligned} y&=1+2^{-p}\\ &=1+\frac1{x-1}=\frac{x}{x-1}. \end{aligned}

Therefore, the correct answer is C.