Questions: Graphs and Functions Domain of a square root function: Basic Find the domain of the function. g(x) = sqrt(x-7) Write your answer using interval notation.

Solution Steps

To find the domain of the function \( g(x) = \sqrt{x-7} \), we need to determine the values of \( x \) for which the expression under the square root is non-negative. This means solving the inequality \( x - 7 \geq 0 \).

The function given is \( g(x) = \sqrt{x-7} \). This is a square root function, and we need to determine the domain of this function.

For the square root function to be defined, the expression inside the square root must be non-negative. Therefore, we need:

\[ x - 7 \geq 0 \]

Solve the inequality \( x - 7 \geq 0 \):

\[ x \geq 7 \]

The domain of the function \( g(x) = \sqrt{x-7} \) is all \( x \) values that satisfy \( x \geq 7 \). In interval notation, this is written as:

\[ [7, \infty) \]

Final Answer