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.
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 $\displaystyle \{x| x\ne \pm 3\}$.