Question 254688
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The domain of a function is the set of numbers that can be input as the value of the independent variable (generally speaking, the "x") for which the function is defined.  Answers b, c, and d do not describe numbers for which *[tex \Large p(x)] is undefined, because, in fact, there are no such numbers.


In general, for any polynomial function, that is a function of the form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ p(x)\ =\ a_0x^n\ +\ a_1x^{n-1}\ +\ \cdots\ +\ a_ix^{n-i}\ +\ \cdots\ +\ a_n]


Where *[tex \Large a_0\ \neq\ 0], the domain is *[tex \Large \{x\,|\,x\,\in\,\R}], which is to say all real numbers.


Where you will see restrictions on the value of the independent variable is when you have a rational function such as:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r(x)\ =\ \frac{f(x)}{g(x)}]


in this case, the domain would be all real numbers <i>except</i> any value that would make *[tex \Large g(x)] equal zero.


Another example would be if you had a function containing a radical with an even  index.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ \sqrt{x\ -\ 1}]


In this case *[tex \Large f] has no real values for *[tex \Large x\ <\ 1], hence the domain is *[tex \Large \{x\,|\,x\,\in\,\R,\ x\ \geq\ 1}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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