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in Differential equations by (50.2k points)

A function f:(0,  (2, ) is defined as f(x) = x2 + 2. Find f–1(x).

1 Answer

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Best answer

Given f(x) = x2 + 2

⇒ f'(x) = 2x > 0 for every x > 0

⇒ f is strictly increasing function.

⇒ f is one-one function.

Also, Rf = (2, ) = Co-domain

⇒ f is onto function.

Thus f is a bijective function.

Therefore, the inverse of the given function is exists. 

Let y = x2 + 2 

⇒ x2 = y – 2 

⇒ x = √(y – 2)

Hence, f–1(x) = √(x – 2) 

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