Question 194813
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The domain is that set of values for which the function is defined.  You have a rational function, so you need to find any values for which the denominator would be zero.  Then the domain is everything else.


Set the denominator equal to zero:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 - 25 = 0]


Factor the difference of two squares:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (x + 5)(x - 5) = 0]


So the denominator is zero if *[tex \LARGE x = \pm5]


Hence, the domain is all real numbers except for 5 and -5.  In set builder notation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \{x | x\ \in\ \R,\ x \neq \pm5\}] 




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