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Specify the Domain of Each Function


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Recall that the DOMAIN of a function is the set of all possible values of the independent variable (input) in the function that allow the function to work. That is, the domain of a function f(x) is the set of all possible x-values which all the function to work and will thus output real y-values. 

     f(x) = x2 - 9 

Note that when finding the domain, if the function contains a fraction the denominator of the fraction cannot equal 0. Also, the values under a square root sign must be positive (since the square root of a negative number yields an imaginary number).

These criteria, however, are not applicable for the function in question since it does not contain a fraction or a square root.

Thus, the domain for this function is

     all real numbers   ==>   { x ¦ all real numbers x }   ==>   (-∞, ∞)