Finding the inverse of a cubic polynomial is equivalent to solving a cubic equation. A special case that is simpler than the general case is the cubic y = f(x) = x³ + ax. Find the inverse of the following cubics using the substitution (known as Vieta’s substitution) x = z - a/(3z). Be sure to determine where the function is one-to-one.

f(x) = x³ + 4x - 1