+6251 $$y=\dfrac{2x+1}{3x-2}$$
First off note that this isn't defined at x=2/3 but other than that it is one to one.
$$(3x-2)y=2x+1$$
$$3xy - 2y = 2x+1$$
$$x(3y-2)=1+2y$$
$$x=\dfrac {1+2y}{3y-2}$$
now just replace x by f-1(x) and y by x to obtain
$$f^{-1}(x)=\dfrac{2x+1}{3x-2}~~\forall x \neq \dfrac 2 3$$
.+6251 $$y=\dfrac{2x+1}{3x-2}$$
First off note that this isn't defined at x=2/3 but other than that it is one to one.
$$(3x-2)y=2x+1$$
$$3xy - 2y = 2x+1$$
$$x(3y-2)=1+2y$$
$$x=\dfrac {1+2y}{3y-2}$$
now just replace x by f-1(x) and y by x to obtain
$$f^{-1}(x)=\dfrac{2x+1}{3x-2}~~\forall x \neq \dfrac 2 3$$
