Find the domain of the function. $$ f(x)=\sqrt{-x+5} $$ Write your answer using interval notation.

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The domain is $$(-∞, 5]$$. To find the domain of the function $$ f(x) = \sqrt{-x + 5} $$, we need to determine the values of $$ x $$ for which the expression inside the square root is non-negative, since the square root function is only defined for non-negative values. We start by setting up the inequality: $$ -x + 5 \geq 0 $$ Next, we solve for $$ x $$: 1. Subtract 5 from both sides: $$ -x \geq -5 $$ 2. Multiply both sides by -1 (remember to reverse the inequality sign): $$ x \leq 5 $$ This tells us that $$ x $$ can take any value less than or equal to 5. Now, we also need to consider if there are any lower bounds for $$ x $$. Since there are no restrictions on how low $$ x $$ can go (the square root will still be defined as long as the expression inside is non-negative), we conclude that $$ x $$ can take any value less than or equal to 5. Thus, the domain of the function in interval notation is: $$ (-\infty, 5] $$

Find the domain of the function. \[ f(x)=\sqrt{-x+5} \] Write your answer using interval notation.

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Find the domain of the function. \[ f(x)=\sqrt{-x+5} \] Write your answer using interval notation.

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