Find the domain of the function. \[ f(x)=\frac{\sqrt{6+x}}{3-3 x} \] Write your answer as an interval or union of intervals

To find the domain of the function \( f(x) = \frac{\sqrt{6+x}}{3-3x} \), we need to ensure two conditions are satisfied: the expression under the square root must be non-negative, and the denominator must not equal zero. 1. **Square Root Condition**: For \( \sqrt{6+x} \) to be defined, we require: \[ 6 + x \geq 0 \implies x \geq -6. \] 2. **Denominator Condition**: The denominator \( 3 - 3x \) must not equal zero: \[ 3 - 3x \neq 0 \implies 3 \neq 3x \implies x \neq 1. \] Combining these two conditions, we have \( x \geq -6 \) and \( x \neq 1 \). The domain of the function in interval notation is: \[ [-6, 1) \cup (1, \infty). \]