Q17 of 215 Page 3

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

We have f: R → (–1, 1) and


Given that f-1 exists.


Let y ϵ (–1, 1) such that f(x) = y





⇒ 102x – 1 = y (102x + 1)


⇒ 102x – 1 = 102xy + y


⇒ 102x – 102xy = 1 + y


⇒ 102x (1 – y) = 1 + y



Taking log10 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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