f(x) = 2x+3/x-4 Work out f ^–1 (x)

first off, replace all x values with y and all y values with x, which gives us, X = 2Y + 3 / Y - 4 rearrange to give, X(Y - 4) = 2Y + 3 expand the bracket, XY - 4X = 2Y + 3 rearrange to get all Y terms on one side, XY -2Y = 4X + 3 factorise to give Y(X - 2) = 4X + 3 and finally rearrange to get, Y = 4X + 3/X - 2