Q. 185.0( 1 Vote )

If f: R (0, 2) defined by is invertible, find f-1.

Answer :

We have f: R (0, 2) and


Given that f-1 exists.


Let y ϵ (0, 2) such that f(x) = y







2e2x = y (e2x + 1)


2e2x = e2xy + y


2e2x – e2xy = y


e2x (2 – y) = y



Taking ln on both sides, we get






We have f(x) = y x = f-1(y)


But, we found f(x) = y


Hence,


Thus,


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