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Let f: X->Ybe an invertible function. Sh...

Let `f: X->Y`be an invertible function. Show that f has unique inverse. (Hint: suppose `g_1( and g)_2`are two inverses of `f`. Then for all `y in Y ,fog_1(y)=I_Y(y)=fog_2(y)`. Use one oneness of `f` ).

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To show that an invertible function \( f: X \to Y \) has a unique inverse, we will follow the steps outlined in the hint provided. ### Step 1: Assume Two Inverses Let \( g_1 \) and \( g_2 \) be two inverses of the function \( f \). By definition of an inverse function, we have: \[ f(g_1(y)) = y \quad \text{for all } y \in Y \] and ...
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