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) x 3 ax Find the inverse of the following cubics using the substitution (known as Vietas substitution) x z a (3z) Be sure to determine where th...

The given function is onetoone so it has an inverse Let y x 3 4x 1 so y 1 x 3 4x Making the suggest ...

Finding the inverse of a cubic polynomial is equivalent to solving a cubic equation. A special case

Question:

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

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