Determine the domain of the function. \( f(x)=\sqrt{4-x} \) Choose the domain of \( f(x) \). A. \( [4, \infty) \) B. \( (-\infty, 4) \) C. \( (-\infty, 4] \) D. \( (-\infty, \infty) \)

1. To determine the domain of \( f(x)=\sqrt{4-x} \), we require the expression under the square root to be non-negative: \[ 4-x \geq 0 \] 2. Solve the inequality: \[ 4-x \geq 0 \quad \Longrightarrow \quad -x \geq -4 \] Multiply both sides by \(-1\) (remember to reverse the inequality), which gives: \[ x \leq 4 \] 3. Therefore, the domain of the function is all real numbers \( x \) such that: \[ x \leq 4 \] In interval notation, this is: \[ (-\infty, 4] \] 4. The correct answer is **C. \( (-\infty, 4] \)**.