Question

Find the domain of -1/x^2-4

Answer 1

Answer:

$\mathbb{R}-\{0\}$

$(-\infty,0)\ U\ (0,+\infty)$

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

$\displaystyle f(x)=-\frac{1}{x^2}-4$

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

$x^2=0$

Or equivalently

x=0

The domain of f can be written as

$\mathbb{R}-\{0\}$

Or also

$(-\infty,0)\ U\ (0,+\infty)$