Question

Find the domain of f(x) = -√x² – 16.-all real numbersx ≥4 or x ≤ 4x24Ox≥4 or x ≤ - 4

Answer 1

Given: A function-

$f(x)=-\sqrt{x^2-16}$

Required: To determine the domain of the function.

Explanation: The domain of a function is the set of all the input values or x-values at which the function f(x) exists.

The square root of a negative number does not give any real value. Hence, the function will exist for-

$\begin{gathered} x^2-16\ge0 \\ x^2\ge16 \\ \Rightarrow x\ge4\text{ or }x\leq-4 \end{gathered}$

Hence, the domain is-

$Domain:\text{ \lparen-}\infty,-4]\cup[4,\infty)$

Final Answer: Option D is correct.