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in Differential equations by (50.3k points)

A function f:R+  [0, 1] is defined as f(x) = x2/(x2 + 1). Find f–1 (x).

1 Answer

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Given f(x) = x2/(x2 + 1)

⇒ f is strictly increasing function. 

⇒ f is one-one function.

⇒ Rf = (0, 1) = Co-domain

⇒ f is onto function.

Thus, f is a bijective function.

⇒ f–1 (x) is exists.

Hence, f-1(x) = √(x/(1 - x)).

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