Questions: Find the domain of the function. f(x)=1/(sqrt(x+4)) What is the domain of f ? A. [-4, infinity) B. [0, infinity) C. (-infinity,-4) U (-4, infinity) D. (-4, infinity)

Find the domain of the function. f(x)=1/(sqrt(x+4)) What is the domain of f ? A. [-4, infinity) B. [0, infinity) C. (-infinity,-4) U (-4, infinity) D. (-4, infinity)
Transcript text: Find the domain of the function. \[ f(x)=\frac{1}{\sqrt{x+4}} \] What is the domain of $f$ ? A. $[-4, \infty)$ B. $[0, \infty)$ C. $(-\infty,-4) \cup(-4, \infty)$ D. $(-4, \infty)$
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Solution

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Solution Steps

Step 1: Identify the expression under the square root

The expression under the square root is $x + 4$.

Step 2: Set the expression greater than or equal to zero

We set the expression greater than or equal to zero: $x + 4 >= 0$.

Step 3: Solve the inequality

Solving the inequality, we find the solution: $x >= -4$.

Step 4: Write the domain in interval notation

Thus, the domain of the function in interval notation is $[-4, \infty)$.

Final Answer:

The domain of the function $f(x) = \sqrt{x + 4}$ is $[-4, \infty)$.

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