Finding the number of rational values a function can take

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SUMMARY

The discussion centers on determining the number of rational values that the expression f(a) + f(b) + f(c) can take, given the conditions of the continuous and differentiable function f(x). It is established that f(a) and f(b) must be irrational values of the form ±√I, where I denotes whole numbers, and that f(c) is fixed at -1.5. The conclusion drawn is that the only combinations that yield rational sums are limited, resulting in a total of three distinct rational values for f(a) + f(b) + f(c).

PREREQUISITES
  • Understanding of continuous and differentiable functions
  • Familiarity with Rolle's Theorem
  • Knowledge of irrational numbers and their properties
  • Basic graphing skills for analyzing function behavior
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  • Study the implications of Rolle's Theorem in depth
  • Explore the properties of continuous functions and their derivatives
  • Learn about the characteristics of irrational numbers and their sums
  • Investigate graphical methods for analyzing function behavior
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Mathematics students, educators, and anyone interested in advanced calculus concepts, particularly those involving continuous functions and rationality in sums of function values.

  • #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.
 
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Likes   Reactions: Titan97
  • #34
That's ok :angel:
 

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