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)=-√(x^2-16)`

Required: To determine the domain of the function.

Step-by-step 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.