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Is f⁻¹ Also Bijective?
publish date: 2026/05/23 21:16:55.669052 UTC
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If \(f: A \to B\) is bijective and \(f^{-1}: B \to A\) is its inverse, what type of function is \(f^{-1}\)?
Correct Answer
Also bijective (one-one and onto)
Explanation
Since \(f^{-1}\) is itself a bijective function: it is injective (if \(f^{-1}(y_1)=f^{-1}(y_2)\) then applying \(f\) gives \(y_1 = y_2\)) and surjective (every element of \(A\) equals \(f^{-1}(f(a))\) for some \(a\)). So \(f\) bijective \(\Rightarrow\) \(f^{-1}\) bijective, and \((f^{-1})^{-1} = f\).
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012