Answer:
![g(x)=-2\sqrt[3]x](https://tex.z-dn.net/?f=g%28x%29%3D-2%5Csqrt%5B3%5Dx)
or
![g(x) = -2f(x)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-2f%28x%29)
Step-by-step explanation:
Given
![f(x) = \sqrt[3]x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5Dx)
Required
Write a rule for g(x)
See attachment for grid
From the attachment, we have:
![(x_1,y_1) = (-1,2)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28-1%2C2%29)
![(x_2,y_2) = (1,-2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%281%2C-2%29)
We can represent g(x) as:
![g(x) = n * f(x)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20n%20%2A%20f%28x%29)
So, we have:
![g(x) = n * \sqrt[3]x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20n%20%2A%20%5Csqrt%5B3%5Dx)
For:
![(x_1,y_1) = (-1,2)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28-1%2C2%29)
![2 = n * \sqrt[3]{-1}](https://tex.z-dn.net/?f=2%20%3D%20n%20%2A%20%5Csqrt%5B3%5D%7B-1%7D)
This gives:
![2 = n * -1](https://tex.z-dn.net/?f=2%20%3D%20n%20%2A%20-1)
Solve for n
![n = \frac{2}{-1}](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7B2%7D%7B-1%7D)
![n = -2](https://tex.z-dn.net/?f=n%20%3D%20-2)
To confirm this value of n, we make use of:
![(x_2,y_2) = (1,-2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%281%2C-2%29)
So, we have:
![-2 = n * \sqrt[3]1](https://tex.z-dn.net/?f=-2%20%3D%20n%20%2A%20%5Csqrt%5B3%5D1)
This gives:
![-2 = n * 1](https://tex.z-dn.net/?f=-2%20%3D%20n%20%2A%201)
Solve for n
![n = \frac{-2}{1}](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7B-2%7D%7B1%7D)
![n = -2](https://tex.z-dn.net/?f=n%20%3D%20-2)
Hence:
![g(x) = n * \sqrt[3]x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20n%20%2A%20%5Csqrt%5B3%5Dx)
![g(x)=-2\sqrt[3]x](https://tex.z-dn.net/?f=g%28x%29%3D-2%5Csqrt%5B3%5Dx)
or:
![g(x) = -2f(x)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-2f%28x%29)
Answer:
-44
Step-by-step explanation:
If the input is -28, that means x = -28, so we plug -28 in for x and solve for y, which is the output:
y = x - 16
y = -28 - 16 = -44
The answer is thus -44.
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Would it be distribution were you multiply the three in? -3(b-7) -3*b and -3*-7 where your answer would be -3b+21
Answer:
-4
Step-by-step explanation:
Use the given value of f(1) to find f(2):
f(2) = f(1) · (-1/2) = (-16)(-1/2) = 8
Now, we can find f(3) using f(2):
f(3) = f(2) · (-1/2) = (8)(-1/2)
f(3) = -4