Need of an example function

Hello,

I need an example of a function f:z1 --> z1; where z1 is a finitely
bounded complex number / real number based set. The function should be
one-one/onto, though it should not have inverse. This means, f(f(z1)) !
= z1. Is there any smooth function which satisfies such a condition.

With Regards,
Reetesh Mukul

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