Inverses of (some) cubics 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 − 2x
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