Question

If $f\left(x\right)=\frac{x}{1+x}$ find range of $f\left(x\right)$

Answer 1

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

$⟹y+xy=xy=x-xyy=(1-y)xx=\frac{y}{1-y}$

This function is not defined when $1-y=0$

So $y\ne 1$

$⟹$ Range is $R-\left\{1\right\}$