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🤖 Ai回答:
To determine the domain of the function \( f(x) = \frac{1}{x^2 4} \), we need to identify the values of \( x \) for which the function is defined、The function is undefined where the denominator is zero because division by zero is not allowed.

The denominator of the function is \( x^2 4 \)、We set the denominator equal to zero and solve for \( x \):

\[
x^2 4 = 0
\]

This is a difference of squares, which can be factored as:

\[
(x 2)(x + 2) = 0
\]

Setting each factor equal to zero gives us the solutions:

\[
x 2 = 0 \quad \text{or} \quad x + 2 = 0
\]

Solving these equations, we get:

\[
x = 2 \quad \text{or} \quad x = -2
\]

Therefore, the function \( f(x) = \frac{1}{x^2 4} \) is undefined at \( x = 2 \) and \( x = -2 \)、The domain of the function is all real numbers except \( x = 2 \) and \( x = -2 \).

In interval notation, the domain is:

\[
(-\infty, -2) \cup (-2, 2) \cup (2, \infty)
\]

Thus, the domain of the function is \(\boxed{(-\infty, -2) \cup (-2, 2) \cup (2, \infty)}\).

Ai作答

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