If $y=\frac{(x+2)}{x-1}$ , then

$y=\frac{x+2}{x-1}$

$yx-y=x+2$

$yx-x=y+2$

$x(y-1)=y+2$

$x=\frac{y+2}{y-1}$

$x=f\left(y\right)$

$f\left(1\right)$ is not defined

$\frac{dy}{dx}=\frac{(x-1).1-(x+2).1}{{\left(x-1\right)}^2}=\frac{-3}{{\left(x-1\right)}^2}<0$

$f\text{'}\left(x\right)<0$, $f\left(x\right)$ is decreasing function

Elements of function $R/\left\{1\right\}$is a Rational number.