Determine the domain of the function. \( f(x)=\sqrt{7-x} \) Choose the domain of \( f(x) \). A. \( [7, \infty) \) B. \( (-\infty, \infty) \) C. \( (-\infty, 7] \) D. \( (-\infty, 7) \)

We have the function \( f(x)=\sqrt{7-x} \). 1. The square root is defined when the expression under the square root is non-negative, so we need: \[ 7-x \geq 0. \] 2. Solving the inequality: \[ 7-x \geq 0 \quad \Longrightarrow \quad -x \geq -7 \quad \Longrightarrow \quad x \leq 7. \] (Multiplying both sides by \(-1\) reverses the inequality.) 3. Thus, the domain of \( f(x) \) is the set of all real numbers \( x \) such that \( x \leq 7 \). In interval notation, this is: \[ (-\infty, 7]. \] Therefore, the correct answer is C. \( (-\infty, 7] \).