Answer
f(x)=$\frac{3x-2}{5x-3}$
x=$\frac{3y-2}{5y-3}$
5xy-3x=3y-2
5xy-3y=3x-2
y(5x-3)=3x-2
y=$\frac{3x-2}{5x-3}$
f$^{-1}$(x)=$\frac{3x-2}{5x-3}$
Work Step by Step
f(x)=$\frac{3x-2}{5x-3}$
x=$\frac{3y-2}{5y-3}$
5xy-3x=3y-2
5xy-3y=3x-2
y(5x-3)=3x-2
y=$\frac{3x-2}{5x-3}$
f$^{-1}$(x)=$\frac{3x-2}{5x-3}$
If you switch the x and y values of this function and simplify you get the same equation, so this function is the inverse of itself.
