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

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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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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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