Specify the Domain of Each Function

Question

f(x)=x^2-9

Not sure where to even start...

Answer 1

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 }   ==>   (-∞, ∞)