Find the domain of the function. \( f(x)=\sqrt{10-2 x} \) What is the domain of \( f \) ? \( \square \) (Type your answer in interval notation.)

To find the domain of the function \( f(x)=\sqrt{10-2x} \), we need to ensure that the expression inside the square root is non-negative, since the square root of a negative number is not defined in the real number system. Therefore, we set up the inequality: \[ 10 - 2x \geq 0 \] Solving for \( x \): 1. Rearranging gives \( 2x \leq 10 \) 2. Dividing by 2 yields \( x \leq 5 \) Thus, \( x \) can take any value up to and including 5. Since there's no lower bound on \( x \) from this inequality, we also include all values less than 5. Therefore, the domain of \( f \) in interval notation is: \[ (-\infty, 5] \] So, the domain of \( f \) is \( \boxed{(-\infty, 5]} \).