Question

How do you find the domain of `f(x) = (x+9)/(x-3)`?

Answer 1

It will be all the real `x` except `x=3`.

Explanation:

The domain represents the set of all possible `x` values that your function can accept.
In this case your function represent a Quotient (a division) with the `x` in the denominator.
The problem with this configuration arises when the denominator becomes equal to zero because we cannot evaluate the quotient (in the Real domain), i.e., divide by zero.
So we say that the domain will be all real `x` except the values that makes the denominator equal to zero, i.e., when:
`x-3=0`
And so when:
`x=3`
So `x=3` will not be allowed or we say that the domain will be all the real `x` except `x=3`.