The answer is -31 over 12.
Answer:
B
Step-by-step explanation:
You could just subtract the numbers from the line. It's simple.
To find the inverse, we swap the variables y and x, then solve for the new y.
3a.
![y=\frac{3}{x-1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7Bx-1%7D)
Swapping the variables:
![x=\frac{3}{y-1}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7By-1%7D)
Solving for y:
![x(y-1)=3 \\ y-1= \frac{3}{x} \\ y=1+\frac{3}{x}](https://tex.z-dn.net/?f=x%28y-1%29%3D3%20%5C%5C%20y-1%3D%20%5Cfrac%7B3%7D%7Bx%7D%20%5C%5C%20y%3D1%2B%5Cfrac%7B3%7D%7Bx%7D%20)
The domain of this inverse is
![x ≠ 0](https://tex.z-dn.net/?f=x%20%E2%89%A0%200)
.
3b.
![y=x^2-1](https://tex.z-dn.net/?f=y%3Dx%5E2-1)
Swapping:
![x = y^2 - 1](https://tex.z-dn.net/?f=x%20%3D%20y%5E2%20-%201)
Solving for y:
![y^2 = x + 1 \\ y = \sqrt{x+1}](https://tex.z-dn.net/?f=y%5E2%20%3D%20x%20%2B%201%20%5C%5C%20y%20%3D%20%5Csqrt%7Bx%2B1%7D%20)
The domain of this inverse is
![x ≥ -1](https://tex.z-dn.net/?f=x%20%E2%89%A5%20-1)
.
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:
![x^3=\frac{y-7}{3} \\ y-7=3x^3 \\ y=3x^3+7](https://tex.z-dn.net/?f=x%5E3%3D%5Cfrac%7By-7%7D%7B3%7D%20%5C%5C%20y-7%3D3x%5E3%20%5C%5C%20y%3D3x%5E3%2B7)
The domain of this inverse is all real numbers.
4a.
![y=\frac{3}{x-1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7Bx-1%7D)
,
![y=1+\frac{3}{x}](https://tex.z-dn.net/?f=y%3D1%2B%5Cfrac%7B3%7D%7Bx%7D)
![y=\frac{3}{(1+\frac{3}{x})-1} \\ y=\frac{3}{(\frac{3}{x})} \\ y=x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B%281%2B%5Cfrac%7B3%7D%7Bx%7D%29-1%7D%20%5C%5C%20y%3D%5Cfrac%7B3%7D%7B%28%5Cfrac%7B3%7D%7Bx%7D%29%7D%20%5C%5C%20y%3Dx)
4c.
![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)
,
![y=3x^3+7](https://tex.z-dn.net/?f=y%3D3x%5E3%2B7)
![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)
x = 10
_____________________________________________