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Mutually Inverse Functions: y = x³ and y = ∛x
publish date: 2026/05/23 21:16:57.525270 UTC
volume_mute
Are \(y = x^3\) and \(y = \sqrt[3]{x}\) mutually inverse functions?
Correct Answer
Yes
Explanation
Yes. Starting from \(y = x^3\), solving for \(x\): \(x = y^{1/3} = \sqrt[3]{y}\). Replacing \(y\) by \(x\) gives the inverse: \(y = \sqrt[3]{x}\). Their graphs are reflections of each other in the line \(y = x\). Verify: \((\sqrt[3]{x})^3 = x\) ✓ and \(\sqrt[3]{x^3} = x\) ✓.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012