Finding Inverse for (x+2)^2(x-3)

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Homework Help Overview

The discussion revolves around the function \( (x+2)^2(x-3) \) and the inquiry into the existence of an inverse for all real numbers. Participants explore whether the function is one-to-one and consider the implications of restricting the domain to potentially allow for an inverse.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the function's one-to-one nature and the implications for its inverse. Some suggest identifying intervals where the function may be one-to-one, while others question the necessity of finding the inverse directly.

Discussion Status

The conversation is active, with participants providing guidance on understanding the function's properties and discussing possible domain restrictions. There is recognition of multiple intervals where the function could be one-to-one, indicating a productive exploration of the topic.

Contextual Notes

There is mention of a specific value where the inverse is undefined, and participants note the importance of graphing the function to understand its behavior. The original poster's approach to taking the square root is questioned, indicating a need for clarification on the problem's requirements.

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Homework Statement



(x+2)^2(x-3) I am asked does an inverse exist for all real numbers? then I am asked can I restrict the domain and force and inverse to exist?

Homework Equations


I said no because the function is not one-to-one when graphed.


The Attempt at a Solution

I thought it I took the square root of the x's in the original equation then this would work.
 
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Okay, I'll warn you that if you don't clean this up you'll get reamed!
You're given a function. Let's call it f(x) and define it to be equal to (x+2)^2(x-3)
Now you're asked to take the inverse. Do that. There is one REAL value of x for which the inverse is undefined. This should be poignantly obvious. Part two of that question will make sense once you figure out part 1.
 
I'm afraid BrendanH has misunderstood the problem. You are not asked to take the inverse and are a whole lot more than ONE value at which that does not have an inverse!

wegnes, you say you have graphed it and know that it does not have an inverse because it is not one-to-one. Excellent! Now, on what intervals is the function one-to-one? There are several of those and so several different ways to restrict the function so that the restiction does have an inverse.

Since the question does not ask you to actually find an inverse, it is not necessary to "take the square root" or anything like that.
 
Thank you! That what I wasn't doing! You are a big help, I apreciate it;o)
 

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