Find the inverse of the function f(x)=(x^3-4)/(x^3-3)

Question

How do I find the inverse of this equation

Answer 1

Let y=(x³-4)/(x³-3), y(x³-3)=x³-4, yx³-3y=x³-4, yx³-x³=3y-4, x³=(3y-4)/(y-1), x=∛((3y-4)/(y-1))=f⁻¹(y).

f⁻¹(x)=∛((3x-4)/(x-1)).