find the domain of f(x)= -\sqrt()x^2 4

1 answer

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:

  1. \( x \geq 2 \)
  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:

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