volume_mute
Match Functions to Their Inverses
publish date: 2026/05/23 21:16:58.066776 UTC
volume_muteMatch each function to its inverse.
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Function f(x)
\(2x\)
\(x^3\)
\(3x - 2\)
\(10^x\)
Inverse f⁻¹(x)
\(\log_{10} x\)
\(\dfrac{x}{2}\)
\(\sqrt[3]{x}\)
\(\dfrac{x + 2}{3}\)
Correct Answer
(1) \(2x\),\(\dfrac{x}{2}\)
(2) \(x^3\),\(\sqrt[3]{x}\)
(3) \(3x - 2\),\(\dfrac{x + 2}{3}\)
(4) \(10^x\),\(\log_{10} x\)
Explanation
Each pair can be verified by checking \(f^{-1}(f(x)) = x\): \(\frac{2x}{2} = x\), \(\sqrt[3]{x^3} = x\), \(\frac{(3x-2)+2}{3} = x\), and \(\log_{10}(10^x) = x\). Also \(y = 10^x\) and \(y = \log_{10} x\) are mutually inverse functions — their graphs are symmetric about \(y = x\).
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012