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. $$ [2, \infty) $$

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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.
The domain of $$ f(x) = \sqrt{2 - x} $$ is all real numbers less than or equal to 2, which is $$ (-\infty, 2] $$.

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. \( [2, \infty) \)

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