Find the domain of the function. $$ u(x)=\sqrt{-8 x+48} $$ Write your answer using interval notation.

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The domain of the function $$ u(x) = \sqrt{-8x + 48} $$ is $$(-∞, 6]$$. To find the domain of the function $$ u(x) = \sqrt{-8x + 48} $$, we need to ensure that 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: $$ -8x + 48 \geq 0 $$ Next, we solve for $$ x $$: 1. Subtract 48 from both sides: $$ -8x \geq -48 $$ 2. Divide both sides by -8. Remember that when we divide by a negative number, we must reverse the inequality sign: $$ x \leq 6 $$ This tells us that $$ x $$ can take any value less than or equal to 6. 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 expression will still be defined for negative values of $$ x $$), we conclude that $$ x $$ can take any value from negative infinity up to 6. Thus, the domain of the function $$ u(x) $$ in interval notation is: $$ (-\infty, 6] $$

Find the domain of the function. \[ u(x)=\sqrt{-8 x+48} \] Write your answer using interval notation.

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Find the domain of the function. \[ u(x)=\sqrt{-8 x+48} \] Write your answer using interval notation.

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