Domain and function True/False ?

**kmerr98277** · July 10th 2012, 01:57 PM

True or false,
The domain of the function f(x) = x^2-9/x is {X|X /= +/-3}. I don't understand this question. Also, what does X|X mean? Thanks.

**Plato** · July 10th 2012, 02:16 PM

Originally Posted by kmerr98277

True or false,
The domain of the function f(x) = x^2-9/x is {X|X /= +/-3}. I don't understand this question. Also, what does X|X mean? Thanks.

$\{X|~X\ne\pm 3\}$ is read as The set of all X such that X is not equal to plus or minus three.

**HallsofIvy** · July 10th 2012, 02:58 PM

It is, however, NOT true that the domain of $(x^2- 9)/x$ is the "set of all x such that x is not equal to plus or minus 3". The (natural) domain of a function is the set of all values of x for which the formula can be calculated. There is no problem with x= 3 or -3: f(3)= 0/3= 0 and f(-3)= 0/(-3)= 0. There is a problem with x= 0 because then the denominator is 0 and we cannot divide by 0. The domain of $(x^2- 9)/x$ is $\{x | x\ne 0\}$ .

If the the problem were were with f the reciprocal, $f(x)= \frac{x}{x^2- 9}$ , then, because $x^2- 9= (x- 3)(x+ 3)$ , the denominator would be 0 at x= 3 or x= -3 and the domain would be $\{x| x\ne \pm 3\}$ .

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