(g-h)(x) = 2x+1 -(<span>x-2)
</span>(g-h)(x) = 2x+1 - x + 2
(g-h)(x) = x + 3
El concepto básico de la función es que puede tomar cualquier número de valores, pero puede devolver solo un valor. La función es como una máquina en la que podemos darle una entrada / algo y obtener una salida o un conjunto de salidas. La entrada o el conjunto de entradas se llama dominio.
Sorry I Don't Speak Spanish That Good
Let
. Then
![|z|=\sqrt{(-\sqrt3)^2+1^2}=2](https://tex.z-dn.net/?f=%7Cz%7C%3D%5Csqrt%7B%28-%5Csqrt3%29%5E2%2B1%5E2%7D%3D2)
lies in the second quadrant, so
![\arg z=\pi+\tan^{-1}\left(-\dfrac1{\sqrt3}\right)=\dfrac{5\pi}6](https://tex.z-dn.net/?f=%5Carg%20z%3D%5Cpi%2B%5Ctan%5E%7B-1%7D%5Cleft%28-%5Cdfrac1%7B%5Csqrt3%7D%5Cright%29%3D%5Cdfrac%7B5%5Cpi%7D6)
So we have
![z=2e^{i5\pi/6}](https://tex.z-dn.net/?f=z%3D2e%5E%7Bi5%5Cpi%2F6%7D)
and the fourth roots of
are
![2^{1/4}e^{i(5\pi/6+k\pi)/4}](https://tex.z-dn.net/?f=2%5E%7B1%2F4%7De%5E%7Bi%285%5Cpi%2F6%2Bk%5Cpi%29%2F4%7D)
where
. In particular, they are
![2^{1/4}e^{i(5\pi/6)/4}=2^{1/4}e^{i5\pi/24}](https://tex.z-dn.net/?f=2%5E%7B1%2F4%7De%5E%7Bi%285%5Cpi%2F6%29%2F4%7D%3D2%5E%7B1%2F4%7De%5E%7Bi5%5Cpi%2F24%7D)
![2^{1/4}e^{i(5\pi/6+2\pi)/4}=2^{1/4}e^{i17\pi/24}](https://tex.z-dn.net/?f=2%5E%7B1%2F4%7De%5E%7Bi%285%5Cpi%2F6%2B2%5Cpi%29%2F4%7D%3D2%5E%7B1%2F4%7De%5E%7Bi17%5Cpi%2F24%7D)
![2^{1/4}e^{i(5\pi/6+4\pi)/4}=2^{1/4}e^{i29\pi/24}](https://tex.z-dn.net/?f=2%5E%7B1%2F4%7De%5E%7Bi%285%5Cpi%2F6%2B4%5Cpi%29%2F4%7D%3D2%5E%7B1%2F4%7De%5E%7Bi29%5Cpi%2F24%7D)
![2^{1/4}e^{i(5\pi/6+6\pi)/4}=2^{1/4}e^{i41\pi/24}](https://tex.z-dn.net/?f=2%5E%7B1%2F4%7De%5E%7Bi%285%5Cpi%2F6%2B6%5Cpi%29%2F4%7D%3D2%5E%7B1%2F4%7De%5E%7Bi41%5Cpi%2F24%7D)
Answer:
(a) Rule: Multiply the input (x) by 2 and add 5 to the result of the product
(b) ![y =2x +5](https://tex.z-dn.net/?f=y%20%20%3D2x%20%2B5)
Step-by-step explanation:
Given
The attached table
Solving (a): The rule of the table in words
First, we calculate the slope (m)
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Using:
![(x_1,y_1) = (2,9)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%20%282%2C9%29)
![(x_1,y_1) = (10,25)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%20%2810%2C25%29)
So, we have:
![m = \frac{25 - 9}{10 - 2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B25%20-%209%7D%7B10%20-%202%7D)
![m = \frac{16}{8}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B16%7D%7B8%7D)
![m=2](https://tex.z-dn.net/?f=m%3D2)
The equation is calculated using:
![y - y_1 =m(x - x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3Dm%28x%20-%20x_1%29)
Using:
![(x_1,y_1) = (6,17)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%286%2C17%29)
We have:
![y - 17 =2(x - 6)](https://tex.z-dn.net/?f=y%20-%2017%20%3D2%28x%20-%206%29)
![y - 17 =2x - 12](https://tex.z-dn.net/?f=y%20-%2017%20%3D2x%20-%2012)
Make y the subject
![y =2x - 12+17](https://tex.z-dn.net/?f=y%20%20%3D2x%20-%2012%2B17)
![y =2x +5](https://tex.z-dn.net/?f=y%20%20%3D2x%20%2B5)
Hence, the rule is:
Multiply the input (x) by 2 and add 5 to the result of the product
(b): The rule, in algebra
As solved in (a), the rule is:
![y =2x +5](https://tex.z-dn.net/?f=y%20%20%3D2x%20%2B5)