Finding the Domain of a Function

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Discussion Overview

The discussion revolves around finding the domain of the function \(\sqrt{(x^2 + 4)/(x^2 - 4)}\). Participants explore the implications of square roots and fractions on determining valid input values for the function.

Discussion Character

  • Exploratory, Conceptual clarification, Homework-related

Main Points Raised

  • Some participants note that a square root cannot have a negative number under it, while a fraction cannot have zero as a denominator.
  • Others express uncertainty about the steps needed to determine the domain despite understanding the restrictions.
  • A later reply prompts participants to consider what specific values of \(x\) would result in a zero denominator and what values would lead to a negative expression under the square root.

Areas of Agreement / Disagreement

Participants generally agree on the restrictions imposed by square roots and fractions, but the discussion remains unresolved regarding the specific steps to find the domain.

Contextual Notes

Participants have not yet detailed the specific values or conditions that would lead to a zero denominator or a negative expression under the square root, leaving those aspects unresolved.

megacat8921
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How do you find the Domain of \sqrt{(x^2 + 4)/(x^2 - 4)} ?
 
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megacat8921 said:
How do you find the Domain of \sqrt{(x^2 + 4)/(x^2 - 4)} ?

What restrictions are implied by a square root? What restrictions are implied by a fraction?
 
Prove It said:
What restrictions are implied by a square root? What restrictions are implied by a fraction?

There cannot be a negative number under the square root and a fraction cannot have zero as a denominator. Knowing that, I still cannot figure out what steps to take to figure the problem out.
 
megacat8921 said:
There cannot be a negative number under the square root and a fraction cannot have zero as a denominator. Knowing that, I still cannot figure out what steps to take to figure the problem out.

That's EXACTLY what you need!

What values of x will give a zero denominator?

What values of x will give something negative under the square root?
 

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