Let \(f:X\to Y\) be a bijective function, and let \(f^{-1}:Y\to X\) be its inverse. Verify the cancellation laws \(f^{-1}(f(x))=x\) for all \(x\in X\) and \(f(f^{-1}(y))=y\) for all \(y\in Y\). Conclude that \(f^{-1}\) is also invertible, and has \(f\) as its inverse (thus \((f^{-1})^{-1}=f\)).
Exercise 3.3.6
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Exercise 3.3.8
= { Exercise-3.3.6 }