Question

Let $f\left(x\right)=\frac{1-x}{1+x}$ then prove that $f\left(f\right(x\left)\right)=x$.

Answer 1

Given,

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

Now $f\left(f\right(x\left)\right)$

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

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

$=\frac{2x}{2}$

$=x$.