volume_mute
f⁻¹ Does NOT Mean 1/f(x)
publish date: 2026/05/23 21:16:55.123643 UTC
volume_mute
True or False: The notation \(f^{-1}(x)\) means the same as \(\frac{1}{f(x)}\).
Correct Answer
False
Explanation
False. The superscript \(-1\) on \(f\) names the inverse function, not the reciprocal. For example, if \(f(x) = 2x\), then \(f^{-1}(x) = \frac{x}{2}\) but \(\frac{1}{f(x)} = \frac{1}{2x}\) — these are different. The inverse function reverses the mapping; the reciprocal merely takes the multiplicative inverse of the output value.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012