Answer:
[tex]\mathbb{R}-\{0\}[/tex]
[tex](-\infty,0)\ U\ (0,+\infty)[/tex]
Step-by-step explanation:
The domain of a Function
Given a real function f(x), the domain of f is made of all the values x can take, such that f exists. The function given in the question is
[tex]\displaystyle f(x)=-\frac{1}{x^2}-4[/tex]
Finding the domain of a function is not possible by giving x every possible value and check if f exists in all of them. It's better to find the values where f does NOT exist and exclude those values from the real numbers.
Since f is a rational function, we know the denominator cannot be 0 because the division by 0 is not defined, so we use the denominator to find the values of x to exclude from the domain.
We set
[tex]x^2=0[/tex]
Or equivalently
x=0
The domain of f can be written as
[tex]\mathbb{R}-\{0\}[/tex]
Or also
[tex](-\infty,0)\ U\ (0,+\infty)[/tex]
