Question

Consider the function $f\left(x\right)=\frac{x-1}{x+1}$. What is $f\left(f\right(x\left)\right)$ equal to?

• A. $x$
• B. $-x$
• C. $-\frac{1}{x}$
• D. None of the above

Answer 1

The correct option is C $-\frac{1}{x}$

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

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

$f\left(f\right(x\left)\right)=\frac{-1}{x}$

hence $Ans$ is $optionC$