SOLUTION: What is the domain? p(x)=x^3-x^2-6. Is it the set {x|x is a real number and x does not equal 6}?

Question 282470: What is the domain? p(x)=x^3-x^2-6. Is it the set {x|x is a real number and x does not equal 6}?
Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
Polynomials have all real numbers as their domains. The question of "what is the domain" is really one asking where is the function defined.
Put 6 into the function. Do you get a "normal" function value? Yes, p(6)=174.

For another example, consider f(x)=1/x. Here we know that the function behaves "funny" around x=0. Moreover, many people are aware of the fact that "we can not divide by zero." Although it takes a bit more math to see why this is true concisely, take a look at the graph and you will see some strange behavior.

A final example, consider g(x)=ln(x). This is the natural log function. ln(x)=y means the same thing as e^y=x. Hence, x is always positive and not 0 as e^y=0 is nonsense.
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