Answer:
The image seems odd (in such a way that I can't be sure of which is the equation for which I must find the domain)
I assume that the equation is:
[tex]f(x) = \frac{x + 1}{(x + 1)*(x - 1)}[/tex]
I select this one because the only important thing here is the denominator, and the denominator is the same in both expressions (in this one is factorized, and in the other one isn't)
Well, when we have a function g(x) and we want to find the domain of g(x), we start by assuming that the domain is the set of all real numbers.
Then we need to see if there are real numbers that make some kind of "problem" with our equation.
These "problems" are non-defined operations, for example, a division by zero.
Then if we have a polynomial in the denominator, like in our case, we need to find the values of x such that the denominator is zero. Because these values generate non-defined operations, these values can't be in the domain, then we will define the domain as the set of all real numbers minus the values that cause problems.
In our case, is easy to see that the denominator is zero when one of the parentheses is equal to zero, and that happens for x = 1 or x = -1
Then the domain will be the set of all real numbers except the numbers 1 and -1
This is written as:
D : { x ∈ R / {1, - 1}}
where:
R / {1, - 1}
Is the set of all real numbers such that the elements 1 and -1 are removed.
