If f(x)=(3x+2)/(5x-3), x∈ R - […] , then

$f(x)=\frac{3x+2}{5x-3}$, $y=\frac{3x+2}{5x-3}$

so $5xy-3y=3x+2$ so $5xy-3x=3y+2$

so $x(5y-3)=3y+2$

so $x=\frac{3y+2}{5y-3}=f^{-1}(y)⇒f^{-1}(x)=\frac{3x+2}{5x-3}$

so $f(x)=f^{-1}(x)$