(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi. I found in the answears that the inverse of function [itex]f(x)=3-\sqrt{x-2}[/itex] is [itex]f^{-1}(x)=(3-x)^{2}+2[/itex] only if we restrict it to [itex]{x:x\leq3}[/itex]. I understand that the restriction is needed because the found inverse is a parabola (and thus not one-to-one function).

My general question (1): how to know/find out algebraically (without drawing graphs) the needed restrictions? Is there a general way, or some intuition?

My special question (for the above case) (2): can I chose the restriction [itex][x:x\geq3][/itex]?

3. The attempt at a solution

No attempt since I regard this as a general mathematical knowledge question.

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# A question about restrictions of inverse functions

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