Questions: Find the domain of the function. f(x)=1/(sqrt(x+14)) The domain of f(x) is (Type your answer in interval notation.)

Find the domain of the function. f(x)=1/(sqrt(x+14)) The domain of f(x) is (Type your answer in interval notation.)
Transcript text: Find the domain of the function. \[ f(x)=\frac{1}{\sqrt{x+14}} \] The domain of $f(x)$ is $\square$ (Type your answer in interval notation.)
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Solution

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Solution Steps

Step 1: Identify the Type of Function

Given \(f(x) = \frac{{1}}{{\sqrt{{g(x)}}}}\), we need \(g(x) > 0\) to find the domain.

Step 2: Solve for the Domain

Setting \(g(x) > 0\), we find the roots of \(g(x)\) are -14.

Final Answer:

The domain of \(f(x)\) is \(x > -14\) if \(g(x)\) has real roots. Otherwise, the domain might be more complex or the function might not have a real domain.

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