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Question
Let f: X → Y be an invertible function. Show that the inverse of f−1 is f, i.e., (f−1)−1 = f.
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Solution
Let f: X → Y be an invertible function.
Then, there exists a function g: Y → X such that gof = IX and fog = IY.
Here, f−1 = g.
Now, gof = IX and fog = IY
⇒ f−1 of = IX and fof−1 = IY
Hence, f−1: Y → X is invertible and f is the inverse of f−1 i.e., (f−1)−1 = f.
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