document.write( "Question 1108339: The formula f(x)= 6x2 can be used to find the surface area of a box, where x is the side length. If the surface area is greater than or equal to 24 in2, but less than or equal to 384 in2, what is the domain of the function?
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Algebra.Com's Answer #723393 by KMST(5328) $\"\"$ $\"About$

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The formula $\"f%28x%29=6x%5E2\"$ can be used to find the surface area of a box, where $\"x\"$ is the side length.
\n" ); document.write( "The domain is the set of $\"x\"$ values where the function is defined.
\n" ); document.write( "As the surface area values mentioned are in square inches, thw $\"x\"$ values would be plugged into the function as inches.
\n" ); document.write( "That justifies the choice not to include units in the steps to calculate the result.
\n" ); document.write( "The phrase \"the surface area is greater than or equal to $\"24+in%5E2\"$ , but less than or equal to $\"384+in%5E2\"$ \" translates as
\n" ); document.write( " $\"24%3C=6x%5E2%3C=384\"$ .
\n" ); document.write( "We can multiply or divide all sides of an inequality by a positive number,
\n" ); document.write( "keeping the sihns the same way,
\n" ); document.write( "to get an equivalent inequality.
\n" ); document.write( "In this case,
\n" ); document.write( " $\"24%2F6%3C=6x%5E2%2F6%3C=384%2F6\"$ --> $\"4%3C=x%5E2%3C=64\"$ .
\n" ); document.write( "As $\"x\"$ is a length in inches, it is a positive number,
\n" ); document.write( "so we can take square root of all sides of that inequality to find
\n" ); document.write( " $\"sqrt%284%29%3C=sqrt%28x%5E2%29%3C=sqrt%2864%29\"$ --> $\"2%3C=x%3C=8\"$ .
\n" ); document.write( "The domain of the function is
\n" ); document.write( " $\"2%3C=x%3C=8\"$ or $\"%22%5B+2+%2C+8+%5D%22\"$ if we leave out the units,
\n" ); document.write( "or $\"2in%3C=x%3C=8in\"$ or $\"%22%5B+2+in+%2C+8+in+%5D%22\"$ if we want to include units. \n" ); document.write( "

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