SOLUTION: 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 3

Algebra ->  Surface-area -> SOLUTION: 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 3      Log On


   

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?
Answer by KMST(5328) About Me  (Show Source):
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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.
The domain is the set of x values where the function is defined.
As the surface area values mentioned are in square inches, thw x values would be plugged into the function as inches.
That justifies the choice not to include units in the steps to calculate the result.
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
24%3C=6x%5E2%3C=384 .
We can multiply or divide all sides of an inequality by a positive number,
keeping the sihns the same way,
to get an equivalent inequality.
In this case,
24%2F6%3C=6x%5E2%2F6%3C=384%2F6 --> 4%3C=x%5E2%3C=64 .
As x is a length in inches, it is a positive number,
so we can take square root of all sides of that inequality to find
sqrt%284%29%3C=sqrt%28x%5E2%29%3C=sqrt%2864%29 --> 2%3C=x%3C=8 .
The domain of the function is
2%3C=x%3C=8 or %22%5B+2+%2C+8+%5D%22 if we leave out the units,
or 2in%3C=x%3C=8in or %22%5B+2+in+%2C+8+in+%5D%22 if we want to include units.