Determine the domain of the function. \( f(x)=\sqrt{2-x} \) Choose the domain of \( f(x) \). A. \( (-\infty, 2) \) B. \( (-\infty, 2] \) C. \( (-\infty, \infty) \) D. \( [2, \infty) \)

1. For the square root function \( f(x)=\sqrt{2-x} \) to be defined, the expression under the square root must be non-negative. This gives the inequality: \[ 2-x\geq 0 \] 2. Solve the inequality: \[ 2-x\geq 0 ~\Longrightarrow~ 2\geq x ~\Longrightarrow~ x\leq 2 \] 3. Therefore, the domain of \( f(x) \) is all real numbers \( x \) such that \( x \leq 2 \). 4. In interval notation, the domain is: \[ (-\infty, 2] \] 5. The correct answer is option B.