Questions: Find the domain of the function. y = x / sqrt(x-6) A. [6, ∞) B. (-∞, ∞) C. All real numbers except 6 D. (6, ∞)

Solution Steps

To find the domain of the function \( y = \frac{x}{\sqrt{x-6}} \), we need to determine the values of \( x \) for which the function is defined. The square root in the denominator implies that \( x-6 \) must be greater than 0 (since the square root of a negative number is not real and division by zero is undefined). Therefore, \( x > 6 \).

• The function is defined for values of \( x \) such that the expression under the square root is positive.
• Solve the inequality \( x - 6 > 0 \) to find the domain.

We are given the function \( y = \frac{x}{\sqrt{x-6}} \). To find the domain, we need to ensure that the expression is defined.

The denominator \( \sqrt{x-6} \) must be greater than zero to avoid division by zero and to ensure the square root is defined. Therefore, we set up the inequality: \[ x - 6 > 0 \]

Solving the inequality \( x - 6 > 0 \) gives: \[ x > 6 \] This means that the function is defined for all \( x \) values greater than 6.

Final Answer