Q. 175.0( 3 Votes )

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

Answer :

We have f: R → (–1, 1) and

Given that f^{-1} exists.

Let y ϵ (–1, 1) such that f(x) = y

⇒ 10^{2x} – 1 = y (10^{2x} + 1)

⇒ 10^{2x} – 1 = 10^{2x}y + y

⇒ 10^{2x} – 10^{2x}y = 1 + y

⇒ 10^{2x} (1 – y) = 1 + y

Taking log_{10} 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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