Questions: Radicals Domain of a square root function: Advanced Find the domain of the function. g(x) = sqrt(28+7x) Write your answer using interval notation.

Solution Steps

To find the domain of the function \( g(x) = \sqrt{28 + 7x} \), we need to ensure that the expression inside the square root is non-negative. This means solving the inequality \( 28 + 7x \geq 0 \). The solution to this inequality will give us the domain of the function in interval notation.

The function \( g(x) = \sqrt{28 + 7x} \) involves a square root. For the square root to be defined, the expression inside the square root must be non-negative. Therefore, we need to solve the inequality:

\[ 28 + 7x \geq 0 \]

To solve the inequality \( 28 + 7x \geq 0 \), we first isolate \( x \):

\[ 7x \geq -28 \]

Next, divide both sides by 7:

\[ x \geq -4 \]

The solution to the inequality \( x \geq -4 \) indicates that the domain of the function \( g(x) \) is all \( x \) values greater than or equal to \(-4\). In interval notation, this is expressed as:

\[ [-4, \infty) \]

Final Answer