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Domain and Range of the Inverse Function
publish date: 2026/05/23 21:16:54.540686 UTC
If \(f: A \to B\) is bijective and \(f^{-1}\) is its inverse, complete the two statements: the domain of \(f^{-1}\) is (1), and the range of \(f^{-1}\) is (2).
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the range of f
the domain of f
Correct Answer
(1) the range of f
(2) the domain of f
Explanation
The inverse reverses the roles of input and output: the domain of \(f^{-1}\) = range of \(f\) (because \(f^{-1}\) accepts the outputs of \(f\)), and the range of \(f^{-1}\) = domain of \(f\) (because \(f^{-1}\) produces the inputs of \(f\)). So \(f^{-1}: B \to A\) exactly reverses the direction of \(f: A \to B\).
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012