It looks like there might be some formatting issues in your function. If you're asking for the domain of the function \( f(x) = -\sqrt{x^2 - 4} \), I can help with that.
To find the domain of the function \( f(x) = -\sqrt{x^2 - 4} \), we need to determine where the expression under the square root is non-negative, since the square root function is only defined for non-negative values.
So, we set up the inequality:
\[ x^2 - 4 \geq 0 \]
This simplifies to:
\[ x^2 \geq 4 \]
Taking the square root of both sides, we find:
\[ |x| \geq 2 \]
This leads to two cases:
- \( x \geq 2 \)
- \( x \leq -2 \)
Thus, the solution can be expressed in interval notation as:
\[ (-\infty, -2] \cup [2, \infty) \]
So, the domain of the function \( f(x) = -\sqrt{x^2 - 4} \) is:
\[ (-\infty, -2] \cup [2, \infty) \]