volume_mute
The Axis Convention for Inverse Functions
publish date: 2026/05/23 21:16:59.610889 UTC
volume_mute
To draw the graph of \(f^{-1}\) with \(x\) as the independent variable (horizontal axis), what must be done to the formula \(x = f^{-1}(y)\)?
Correct Answer
Replace y by x so that f⁻¹ is expressed as y = f⁻¹(x)
Explanation
By convention, in \(y = f^{-1}(x)\), \(x\) is the independent variable (horizontal axis) and \(y\) is the dependent variable (vertical axis) — the same convention as for \(f\). Replacing \(y\) by \(x\) in \(x = f^{-1}(y)\) achieves this. The resulting curve \(y = f^{-1}(x)\) is the reflection of \(y = f(x)\) across the line \(y = x\).
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012