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Answer: ![y = \sqrt[3]{4x+8}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7B4x%2B8%7D)
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All of 4x+8 is under a cube root sign.
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Work Shown:
To find the inverse, we swap x and y, then solve for y.
![y = \frac{1}{4}x^3 - 2\\\\x = \frac{1}{4}y^3 - 2\\\\x+2 = \frac{1}{4}y^3\\\\4(x+2) = y^3\\\\4x+8 = y^3\\\\y^3 = 4x+8\\\\y = \sqrt[3]{4x+8}\\\\](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B4%7Dx%5E3%20-%202%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B1%7D%7B4%7Dy%5E3%20-%202%5C%5C%5C%5Cx%2B2%20%3D%20%5Cfrac%7B1%7D%7B4%7Dy%5E3%5C%5C%5C%5C4%28x%2B2%29%20%3D%20y%5E3%5C%5C%5C%5C4x%2B8%20%3D%20y%5E3%5C%5C%5C%5Cy%5E3%20%3D%204x%2B8%5C%5C%5C%5Cy%20%3D%20%5Csqrt%5B3%5D%7B4x%2B8%7D%5C%5C%5C%5C)
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Side note:
If 
and ![g(x) = \sqrt[3]{4x+8}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Csqrt%5B3%5D%7B4x%2B8%7D)
, then 
and 
for all x values in the domain. Effectively, you use function composition to confirm that we have the correct inverse equation.
Answer:
6.3 x 10^-1 is the solution
Answer:
5x - 9
Step-by-step explanation:
The area of the rectangle is:
(1)
The area of the rectangle is the product of length (L) and width (W):
where 
, and the width must be in the form 
.
We need to find the values of a and b. If we calculate the product of L and W, we get:
We know that this equation must be equivalent to (1), so we immediately see that:
- the coefficient of the second order term, 
, must be 35, so
- the zero-order term must be equal to -18, so we have
- We can verify that using a=5 and b=-9, the coefficient of the first-order term corresponds to -53:
So, the width is
W = 5x - 9
U want this simplified???
Hey!
To find the area of Jamal's bed, we must multiply the dimensions together:
27 × 36 = 972
So, the area of the bottom of his bed is 972 square inches.
