Let f : X → Y be an invertible function. Show that the inverse of f-1 is f, i.e., (f-1)-1 = f.
Let f : X → Y be an invertible function. Show that the inverse of f-1 is f, i.e., (f-1)-1 = f.
Solution and Explanation
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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