Answer: (-∞,-1) ∪ (0,+∞)
Step-by-step explanation: The representation fog(x) is a representation of composite function, meaning one depends on the other.
In this case, fog(x) means:
fog(x) = f(g(x))
fog(x) =
This is the function fog(x).
The domain of a function is all the values the independent variable can assume.
For fog(x), denominator can be zero, so:
If x = 0, the function doesn't exist.
<u>Therefore, the domain of this function is: </u><u>-∞ < -1 or x > 0</u>
Answer:
26 ft square by 13 ft high
Step-by-step explanation:
The tank will have minimum surface area when opposite sides have the same total area as the square bottom. That is, their height is half their width. This makes the tank half a cube. Said cube would have a volume of ...
2·(8788 ft^3) = (26 ft)^3
The square bottom of the tank is 26 ft square, and its height is 13 ft.
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<em>Solution using derivatives</em>
If x is the side length of the square bottom, the height is 8788/x^2 and the area is ...
x^2 + 4x(8788/x^2) = x^2 +35152/x
The derivative of this is zero when area is minimized:
2x -35152/x^2 = 0
x^3 = 17576 = 26^3 . . . . . multiply by x^2/2, add 17576
x = 26
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As the attached graph shows, a graphing calculator can also provide the solution.
