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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-one ness of `f` ).

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Let `f: X → Y` be an invertible function.
Also, suppose f has two inverses (say `g1` and `g2`).
Then, for all `y in Y`, we have:
`fog_1(y) = I_Y`
`fog_2(y) = I_Y`
`:. f(g_1(y)) = f(g_2(y))`
As `f` is invertible, `f` is one-one. `:. g_1(y) = g_2(y)`
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