Given f:x -> (x-1)(x-3), for x ≤ c

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To determine the largest possible value of c for which the inverse of the function f(x) = (x-1)(x-3) exists, it is crucial to ensure that f is one-to-one. The discussion emphasizes the importance of graphing the function to visualize its behavior and identify intervals where it is monotonic. An inverse fails to exist if the function is not single-valued, which can occur if it has a horizontal line intersecting the graph at multiple points. Participants highlight that the domain of f must equal the range of its inverse for it to exist. Understanding these concepts is essential for solving the problem effectively.
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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.


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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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