Given f:x -> (x-1)(x-3), for x ≤ c

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Homework Help Overview

The problem involves the function f defined as f:x -> (x-1)(x-3) for x ≤ c, with the goal of determining the largest possible value of c for which the inverse of f exists.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants suggest drawing the graph of the function to visualize its behavior and discuss conditions under which an inverse may not exist. Questions are raised about the relationship between the domain of f and the range of its inverse, as well as the necessity for f to be single-valued.

Discussion Status

The discussion is ongoing, with participants exploring graphical representation and the fundamental properties required for the existence of an inverse function. There is no explicit consensus yet, but some guidance regarding the importance of single-valued functions has been provided.

Contextual Notes

Participants are considering the implications of the function's domain and its graphical representation, which may influence the determination of c. There is an emphasis on understanding the conditions under which the inverse function can be defined.

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Homework Statement



Given f:x -> (x-1)(x-3), for x ≤ c. Find the largest possible value of c for which the inverse of f exists.


Homework Equations





The Attempt at a Solution



I have no idea on this... can anyone help me?
 
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Hi Michael! :wink:

Draw the graph … what does it look like?

And how can an inverse fail to exist? :smile:
 


tiny-tim said:
Hi Michael! :wink:

Draw the graph … what does it look like?

Have i drawn the graph for f and inverse of f, what should i do next?

tiny-tim said:
And how can an inverse fail to exist?

For an inverse to exist, domain if f = range of f-1, correct me if i am wrong. ><
 
ah, no, the really important thing is that f must be single-valued. :wink:
 

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