Finding a value that will make a function continuous

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Discussion Overview

The discussion revolves around the conditions for a function to be continuous, specifically focusing on determining a value of 'a' that ensures continuity at the point x=2. Participants explore the implications of continuity in relation to function values and provide mathematical reasoning.

Discussion Character

  • Technical explanation, Conceptual clarification, Mathematical reasoning

Main Points Raised

  • One participant suggests that for x > 2, any value of 'a' should make the function continuous, seeking clarification on this point.
  • Another participant proposes a specific equation, 5(2)-1 = a(2)^2+1, as a method to solve for 'a'.
  • A subsequent participant confirms that solving the equation yields a = 2 and requests an explanation of the intuition behind using that specific equation.
  • It is noted that for the function to be continuous at x=2, the values of the function must be equal at that point.

Areas of Agreement / Disagreement

Participants appear to agree on the necessity of equal function values for continuity at x=2, but there is no consensus on the broader implications of continuity for values of 'a' when x > 2.

Contextual Notes

The discussion does not clarify the specific form of the function or the assumptions underlying the continuity conditions, leaving some aspects unresolved.

shle
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Hi All, just a question regarding continuous functions.
From what I understand if x > 2, then any value of 'a' should make this function continuous? Any clarification would be very helpful!
Thanks in advance!
 

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Try 5(2)-1 = a(2)^2+1 solve for a
 
Thank you, I get a = 2. Can you please explain to me the intuition behind that? Why is it that I have to use 5(2)-1 = a(2)^2+1 and solve for a?
 
For the function to be continuous at x=2, then they must be equal at that point.
 

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