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.

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- Jul 10th 2012, 01:57 PMkmerr98277Domain and function True/False ?
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. - Jul 10th 2012, 02:16 PMPlatoRe: Domain and function True/False ?
- Jul 10th 2012, 02:58 PMHallsofIvyRe: Domain and function True/False ?
It is, however, NOT true that the domain of $\displaystyle (x^2- 9)/x$ 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 $\displaystyle (x^2- 9)/x$ is $\displaystyle \{x | x\ne 0\}$.

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