Question

Let $f(x)=\frac{x-1}{x+1}$ then $f(f(x))$ is

• A. $\frac{1}{x}$
• B. $-\frac{1}{x}$
• C. $\frac{1}{x+1}$
• D. $\frac{1}{x-1}$

Answer 1

Answer: (B)

$f(f(x))=\frac{f(x)-1}{f(x)+1}=\frac{\frac{x-1}{x+1}-1}{\frac{x-1}{x+1}+1}$
$=\frac{x-1-x-1}{x-1+x+1}=\frac{-2}{2x}=\frac{-1}{x}$