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in Differential equations by (50.2k points)

A function f:[2,  [5, ) is defined as f(x) = x2 – 4x + 9. Find its inverse.

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Given f(x) = x2 – 4x + 9

⇒ f'(x) = 2x – 4 ≥ 0 for all x in Df 

 f is strictly increasing function. 

 f is one-one function. 

Also, Rf = [5, ) = Co-domain 

 f is onto function. 

Therefore, f is a bijective function.  

Hence, its inverse is exists. 

 Let y = x2 – 4x + 5 

 x2 – 4x + (5 – y) = 0

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