How do you find the f(x) inverse using fractions?

For example.. 1) switch places of x and y. x=3y+1 x=3 y +1
2) try to solve for y. so multiply the denominator by x to get rid of it
3) after multiplying, ur left with xy+x=3 x y + x=3
4) that converts to 2xy= x y =3
5) get rid of 2x on left by placing it on the right
6) convert y to inverse function