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megacat8921
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How do you find the Domain of \sqrt{(x^2 + 4)/(x^2 - 4)} ?
megacat8921 said:How do you find the Domain of \sqrt{(x^2 + 4)/(x^2 - 4)} ?
Prove It said:What restrictions are implied by a square root? What restrictions are implied by a fraction?
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.
The domain of a function is the set of all possible input values (or independent variables) for which the function is defined. It is the set of values that can be used as input to the function to produce an output.
To determine the domain of a function algebraically, you must identify any values that would result in an undefined output. These may include division by zero, square roots of negative numbers, or logarithms of non-positive numbers. Once these values are identified, the domain is the set of all real numbers excluding these values.
No, a function can only have one domain. The domain is a set of input values that correspond to unique output values. If a function has multiple domains, it would mean that a single input value could produce multiple output values, which goes against the definition of a function.
The most common types of domains are the natural domain, which includes all real numbers for which the function is defined, and the restricted domain, which is a subset of the natural domain and excludes certain values that would result in an undefined output.
Yes, a function can have an empty domain if there are no input values for which the function is defined. This can occur when there are restrictions on the domain, such as the square root of a negative number, or when the function is undefined for all real numbers.