Question

Consider a function$f:x\to \frac{x+a}{x-1}:x\in R-1\}$

where $a$ is a real constant, If $f$ is not a constant function

answer the following If $f^{-1}$ exists, enter $1$ otherwise $0$.

Answer 1

$f:x\to \frac{x+a}{x-1}:x\in R-\left\{1\right\}$

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

$y(x-1)=x+a,$

$yx-x=a+y$

$x=\frac{y+a}{y-1}$ inverse exists.