Find the domain of the function. \[ f(x)=\sqrt{50-5 x} \] What is the domain of \( f \) ? \( \square \) (Type your answer in interval notation.)

To find the domain of the function \( f(x) = \sqrt{50 - 5x} \), we need to ensure that the expression under the square root is non-negative. This means we set up the following inequality: \[ 50 - 5x \geq 0 \] Solving for \( x \): 1. Subtract 50 from both sides: \[ -5x \geq -50 \] 2. Divide by -5 (remember to flip the inequality): \[ x \leq 10 \] The domain is all values of \( x \) that satisfy this condition, so we also need to ensure that \( 50 - 5x \) stays within the square root. The smallest \( x \) can be is when \( 50 - 5x = 0 \), which is at \( x = 10 \). Thus, the domain in interval notation is: \[ (-\infty, 10] \]