Questions: Find the domain of the function. (Enter your answer using interval notation.)
g(x) = sqrt(4+x) / (7-x)
Transcript text: Find the domain of the function. (Enter your answer using interval notation.)
\[
g(x)=\frac{\sqrt{4+x}}{7-x}
\]
Solution
Solution Steps
Step 1: Identify the restrictions for the square root
The expression under the square root, \( 4 + x \), must be non-negative. Therefore:
\[
4 + x \geq 0
\]
\[
x \geq -4
\]
Step 2: Identify the restrictions for the denominator
The denominator, \( 7 - x \), cannot be zero. Therefore:
\[
7 - x \neq 0
\]
\[
x \neq 7
\]
Step 3: Combine the restrictions
The domain of \( g(x) \) is all real numbers \( x \) such that \( x \geq -4 \) and \( x \neq 7 \). In interval notation, this is:
\[
[-4, 7) \cup (7, \infty)
\]