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