Write the domain and range for the square root function \( y=6 \sqrt{2 x-7}-2 \) ? Enter any fractions as improper fractions. (1 point) The domain is \( \{x \mid x \geq \square\} \) and the range is \( \{y \mid y \geq \square \). Check answer Remaining Attempts : 3

To determine the domain of the function \( y=6 \sqrt{2 x-7}-2 \), we need to ensure the expression inside the square root is non-negative. Setting \( 2x - 7 \geq 0 \) gives us \( x \geq \frac{7}{2} \). Thus, the domain is \( \{x \mid x \geq \frac{7}{2}\} \). For the range, we know that the square root function outputs values starting from zero. Multiplying by 6 and then subtracting 2 means the minimum value of \( y \) occurs when the square root is zero (i.e., at \( x = \frac{7}{2} \)). Therefore, the range is \( \{y \mid y \geq -2\} \).