
Dan V. answered 09/27/15
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Licensed HS Math Teacher, Master of Arts, 20+ years experience
The implied domain of a function is assumed to be the set of real numbers for which the function could be defined. Sometimes the domain is restricted even further.
For most functions, the implied domain IS the set of real numbers. But there are a few types of functions that require additional restriction.
Radical functions with even indices cannot be evaluated for negative valued expressions, so you must determine when the expression under the radical will be non-negative.
Rational functions cannot be evaluated for any variable that makes the denominator equal to 0. So you would need to determine when any denominator in the function would be equal to zero.
Logarithmic functions cannot be evaluated for negative valued expressions, so you must determine when the expression in the logarithm will be non-negative.
The example you gave is a rational function. Determine when the denominator will be zero and exclude such values from the domain.