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**UJJWAL** Thank you for reading my proof. I understand it would be a bit unclear because i don't know about Latex so could not put it in a nice mathematical form. I am learning it and hopefully things would change.

I indeed needed the answer to whether i can construct the inverse function or not. The thing is that i needed the answer very rigorously. You know many people mistake the concept of an inverse function. The inverse of a function is defined in terms of the left inverse and the right inverse.