Question 193816
<font face="Garamond" size="+2">

Presuming that your function is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x) = \frac{1}{x + 2}]


rather than:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x) = \frac{1}{x} + 2]


you are <b><i>almost</i></b> correct.  What you did is express a restriction on the value of the variable, i.e. you told us what <b><i>x</i></b> is <b>not</b>, whereas the domain needs to be an expression of what <b><i>x</i> can be</b>.  The difference is subtle, but important.


There are two commonly accepted ways of doing this.  First, set builder notation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \{x\ |\ x\ \in\ \R,\ x \neq -2}]


Which reads, "the set of all x such that x is an element of the set of real numbers and x is not equal to -2."


Or you can use interval notation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (-\infty,-2)\ \large{\cup\ }\LARGE (-2,\infty)]


to say that the domain is the union of the two intervals from minus infinity to -2 (not inclusive) and -2 (not inclusive) to infinity.




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