Question

If $f\left(x\right)=\frac{x-3}{x+1}$, then $f\left[f\left\{f\right(x\left)\right\}\right]$ equals

• A. $x$
• B. $-x$
• C. $\frac{x}{2}$
• D. $-\frac{1}{x}$

Answer 1

The correct option is A $x$

$f\left(f\right(x\left)\right)=\frac{\frac{x-3}{x+1}-3}{\frac{x-3}{x+1}+1}$

$=\frac{x+3}{1-x}$

$f\left(f\right(f\left(x\right)\left)\right)$ $=\frac{\frac{x+3}{1-x}-3}{\frac{x+3}{1-x}+1}$

$=\frac{4x}{4}=x$