Find the domain of $f\left(x\right)=\sqrt{x+4}$ . Express your answer using interval notation.

• A. Dom: $\left[4,\infty\right)$
• B. Dom: $\left[-4,2\right]$
• C. Dom: $\left[2,4\right]$
• D. Dom: $\left[-4,\infty\right)$

Answer: (D)

Verified step by step guidance

1. Identify the function given: \( f(x) = \sqrt{x + 4} \). This is a square root function.
2. Recall that the expression inside the square root must be non-negative for the function to be defined. Therefore, set up the inequality: \( x + 4 \geq 0 \).
3. Solve the inequality \( x + 4 \geq 0 \) to find the values of \( x \) for which the function is defined. Subtract 4 from both sides to get \( x \geq -4 \).
4. The domain of the function \( f(x) = \sqrt{x + 4} \) is all values of \( x \) that satisfy \( x \geq -4 \).
5. Express the domain in interval notation: \( [-4, \infty) \). This means the function is defined for all \( x \) starting from \(-4\) and extending to positive infinity.