Finding the number of rational values a function can take

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Homework Help Overview

The problem involves a continuous and differentiable function ##f(x)## that takes specific forms at points ##a## and ##b##, with additional conditions on its values and behavior. The goal is to determine the number of rational values that the expression ##f(a) + f(b) + f(c)## can take, given that ##f(c) = -1.5## and other constraints.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the implications of the function's behavior between points ##a##, ##b##, and ##c##, particularly regarding the signs of ##f(x)## and its derivative. There are questions about the continuity of the function and the possibility of roots within certain intervals. Some participants explore the conditions under which ##f(a)## and ##f(b)## can be rational, given their defined forms.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the function's behavior and the implications of the conditions provided. Some guidance has been offered regarding the relationships between the values of ##f(a)## and ##f(b)##, but no consensus has been reached on the final number of rational values.

Contextual Notes

There are constraints regarding the values that ##f(a)## and ##f(b)## can take, as well as the requirement that ##|f(a)| \leq |f(b)|##. The nature of the values being of the form ##^+_-\sqrt{I}## is also under discussion, with implications for the rationality of their sums.

  • #31
Titan97 said:
what is that supposed to mean?
The question in the OP is
Titan97 said:
The number of rational values that f(a)+f(b)+f(c) can take is?
Given what you have found, why do you the answer is 3 instead of 6?
 
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  • #32
0 - 3/2 - √2 is not a rational number
 
  • #33
Titan97 said:
0 - 3/2 - √2 is not a rational number
Whoops - forgot that bit. Sorry for the noise.
 
  • Like
Likes   Reactions: Titan97
  • #34
That's ok :angel:
 

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