Questions: Find the domain of the function. (Enter your answer using interval notation.) g(x) = sqrt(4+x) / (7-x)

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.) \[ g(x)=\frac{\sqrt{4+x}}{7-x} \]
failed

Solution

failed
failed

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: \[ [-4, 7) \cup (7, \infty) \]

Final Answer

\(\boxed{[-4, 7) \cup (7, \infty)}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful