$[20]8.$ Suppose that a function is given as follows: $f(x)=\frac{1}{x-1},x>1.$

$8($a$)$ Find the inverse, $f^{-1}(x)$ and state the domain and range of $f^{-1}.$

$f^{-1}(x)=\frac{1}{x-1}$

$(2)y=\frac{1}{x-1}(x-1)$

$x-1=\frac{1}{y}1,\frac{xb}{yy}$

$x=\frac{1}{y}1,f^{-1}(x)=\frac{1}{x}$

$y=\frac{1}{x}1,x0,f^{-1}(x)=\frac{1}{x}1$

$(-1)y$

V

$($b$)$ Sketch the graphs of fand $f^{-1}$ by specifing the asymptotes $($with the docted liges$).$

Asymptotex $q,y=$

$f()=$

$z(1)=\frac{1}{1}=\frac{1}{2}=0$

$((-1)=-1$

$(t-1{)}^2-\frac{2}{2}{2}^3-\frac{1}{3}=$

$f^{-1}(2)\frac{1}{3},1=\frac{3}{5}$

$f^{-1}(-2)\frac{1}{-2}1=\frac{1}{2}$