A semicircle with a diameter of 8 meters is shown. A smaller semicircle with a diameter of 4 meters is cut out of the larger sem
2 answers:
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To find the inverse, we swap the variables y and x, then solve for the new y.
3a.
Swapping the variables:
Solving for y:
The domain of this inverse is
.
3b.
Swapping:
Solving for y:
The domain of this inverse is
.
3c.![y=\sqrt[3]{\frac{x-7}{3}}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B%5Cfrac%7Bx-7%7D%7B3%7D%7D)
Swapping:![x=\sqrt[3]{\frac{y-7}{3}}](https://tex.z-dn.net/?f=x%3D%5Csqrt%5B3%5D%7B%5Cfrac%7By-7%7D%7B3%7D%7D)
Solving for y:
The domain of this inverse is all real numbers.
4a., 
4c., 
![y=\sqrt[3]{\frac{(3x^3+7)-7}{3}} \\ y=\sqrt[3]{\frac{3x^3}{3}} \\ y=\sqrt[3]{x^3} \\ y=x](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B%283x%5E3%2B7%29-7%7D%7B3%7D%7D%20%5C%5C%20y%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3x%5E3%7D%7B3%7D%7D%20%5C%5C%20y%3D%5Csqrt%5B3%5D%7Bx%5E3%7D%20%5C%5C%20y%3Dx)
![y=3(\sqrt[3]{\frac{x-7}{3}})^3+7 \\ y = 3({\frac{x-7}{3}})+7 \\ y = (x-7)+7 \\ y=x](https://tex.z-dn.net/?f=y%3D3%28%5Csqrt%5B3%5D%7B%5Cfrac%7Bx-7%7D%7B3%7D%7D%29%5E3%2B7%20%5C%5C%20y%20%3D%203%28%7B%5Cfrac%7Bx-7%7D%7B3%7D%7D%29%2B7%20%5C%5C%20y%20%3D%20%28x-7%29%2B7%20%5C%5C%20y%3Dx)
3a.
Swapping the variables:
Solving for y:
The domain of this inverse is
3b.
Swapping:
Solving for y:
The domain of this inverse is
3c.
Swapping:
Solving for y:
The domain of this inverse is all real numbers.
4a.
4c.