Find the domain of the following function.
\[
g(x)=\frac{2}{\sqrt{5+x}}
\]
The domain is
(Type your answer in interval notation.)
Answer
\(\boxed{\text{Final Answer: The domain of the function is } (-5, \infty)}\)
Step 1 ：The function is given as \(g(x)=\frac{2}{\sqrt{5+x}}\).
Step 2 ：The denominator of a function cannot be zero and the value under a square root cannot be negative for real numbers.
Step 3 ：The denominator is \(\sqrt{5+x}\). This will be zero when \(5+x=0\) and negative when \(5+x<0\).
Step 4 ：Solving these equations, we find that the value that makes the denominator zero is -5 and there are no values that make the denominator negative.
Step 5 ：Therefore, the domain of the function is all real numbers greater than -5.
Step 6 ：\(\boxed{\text{Final Answer: The domain of the function is } (-5, \infty)}\)
