Finding the Domain of a Function

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SUMMARY

The domain of the function \(\sqrt{\frac{x^2 + 4}{x^2 - 4}}\) is determined by the conditions that the expression under the square root must be non-negative and the denominator cannot be zero. Specifically, the denominator \(x^2 - 4\) cannot equal zero, leading to restrictions at \(x = 2\) and \(x = -2\). Additionally, the expression \(x^2 + 4\) is always positive, thus the only restrictions on the domain arise from the denominator. Therefore, the domain is all real numbers except \(x = 2\) and \(x = -2\).

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  • Understanding of square root functions
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  • Familiarity with identifying restrictions in functions
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  • Learn about rational functions and their restrictions
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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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