Let f(x) = x+1x-1. Then for x^2 1, f(-x) is

We find f(-x) = -x+1-x-1 = x-1x+1 = 1f(x), so the answer is 1f(x).

smc

algebra intermediate

Problem

Let

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

. Then for

x^{2} \neq = 1, f (- x)

(A)

\frac{1}{f ( x )}

(B)

- f (x)

(C)

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

(D)

- f (- x)

Solution

We find

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

, so the answer is

\frac{1}{f ( x )}

Final answer