Q18 of 215 Page 3

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

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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