Question

If the inverse of the rational function $f\left(x\right)=\frac{x+1}{x-1}$ is $\frac{x+m}{x-m}$.Find the value of $m$

Answer 1

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

replace x to y and y to x, we get inverse of the function

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

$\therefore m=1$