![\bf f(x) = 4(x + 7)^2(x - 7)^3\implies 0 = 4(x + 7)^2(x - 7)^3 \\\\\\ 0=(x+7)^2(x-7)^3\implies \begin{cases} 0=(x+7)^7\\ \qquad 0=(x+7)(x+7)\\ \qquad -7=x\\ \qquad -7=x\\ ----------\\ 0=(x-7)^3\\ \qquad 0=(x-7)(x-7)(x-7)\\ \qquad 7=x\\ \qquad 7=x\\ \qquad 7=x \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%20%3D%204%28x%20%2B%207%29%5E2%28x%20-%207%29%5E3%5Cimplies%200%20%3D%204%28x%20%2B%207%29%5E2%28x%20-%207%29%5E3%0A%5C%5C%5C%5C%5C%5C%0A0%3D%28x%2B7%29%5E2%28x-7%29%5E3%5Cimplies%20%0A%5Cbegin%7Bcases%7D%0A0%3D%28x%2B7%29%5E7%5C%5C%0A%5Cqquad%200%3D%28x%2B7%29%28x%2B7%29%5C%5C%0A%5Cqquad%20-7%3Dx%5C%5C%0A%5Cqquad%20-7%3Dx%5C%5C%0A----------%5C%5C%0A0%3D%28x-7%29%5E3%5C%5C%0A%5Cqquad%200%3D%28x-7%29%28x-7%29%28x-7%29%5C%5C%0A%5Cqquad%207%3Dx%5C%5C%0A%5Cqquad%207%3Dx%5C%5C%0A%5Cqquad%207%3Dx%0A%5Cend%7Bcases%7D)
the -7 is found there twice, so it has a multiplicity of 2
the +7 is there thrice, so it has multiplicity of 3
Answer:
D
Step-by-step explanation:
Think about the question, you can't say that i am wong.
Answer:
Vertex: (-1/2, -25/4)
Focus: (-1/2, -6)
Axis of Symmetry: x=-1/2
Directrix: y=-13/2
Step-by-step explanation:
x = -2, -1, -1/2, 1, 2
y = -4, -6, -25/4, -4, 0
Answer:
<em>Choice: B.</em>
Step-by-step explanation:
<u>Operations With Functions</u>
Given the functions:
![f(x)=\sqrt[3]{12x+1}+4](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B3%5D%7B12x%2B1%7D%2B4)
![g(x)=\log(x-3)+6](https://tex.z-dn.net/?f=g%28x%29%3D%5Clog%28x-3%29%2B6)
The function (g-f)(x) can be obtained by replacing both functions and subtracting them as follows:
![(g-f)(x)= g(x) - f(x)](https://tex.z-dn.net/?f=%28g-f%29%28x%29%3D%20g%28x%29%20-%20f%28x%29)
![(g-f)(x)= \log(x-3)+6 - (\sqrt[3]{12x+1}+4)](https://tex.z-dn.net/?f=%28g-f%29%28x%29%3D%20%5Clog%28x-3%29%2B6%20-%20%28%5Csqrt%5B3%5D%7B12x%2B1%7D%2B4%29)
Operating:
![(g-f)(x)= \log(x-3)+6 - \sqrt[3]{12x+1}-4](https://tex.z-dn.net/?f=%28g-f%29%28x%29%3D%20%5Clog%28x-3%29%2B6%20-%20%5Csqrt%5B3%5D%7B12x%2B1%7D-4)
Joining like terms:
![\boxed{(g-f)(x)= \log(x-3) - \sqrt[3]{12x+1}+2}](https://tex.z-dn.net/?f=%5Cboxed%7B%28g-f%29%28x%29%3D%20%5Clog%28x-3%29%20-%20%5Csqrt%5B3%5D%7B12x%2B1%7D%2B2%7D)
Choice: B.