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

The domain and range for the function \( y = 6 \sqrt{2x - 7} - 2 \) are determined as follows: **Domain:** The expression inside the square root must be non-negative: \[ 2x - 7 \geq 0 \implies 2x \geq 7 \implies x \geq \frac{7}{2} \] So, the domain is: \[ \{x \mid x \geq \frac{7}{2}\} \] **Range:** The square root function \( \sqrt{2x - 7} \) is always non-negative. Multiplying by 6 keeps it non-negative: \[ 6 \sqrt{2x - 7} \geq 0 \] Subtracting 2 shifts the range down by 2: \[ y = 6 \sqrt{2x - 7} - 2 \geq -2 \] So, the range is: \[ \{y \mid y \geq -2\} \] **Final Answer:** The domain is \( \{x \mid x \geq \frac{7}{2}\} \) and the range is \( \{y \mid y \geq -2\} \).