So all positive integers is the domain (the number you can use)
and the range (the numbers you get when you put the numbers in the domain in) is all positive integers more than 2
Answer:
![f(x) = {x}^{3} + 3 {x}^{2} - x -3](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7Bx%7D%5E%7B3%7D%20%20%2B%203%20%7Bx%7D%5E%7B2%7D%20%20-%20x%20-3)
Step-by-step explanation:
The given polynomial has zeros at:
x=−3, x=−1, and x=1.
This means that:
x+3, x+1, and x-1 are all factors of this polynomial.
The factored form of this polynomial is :
![f(x) = (x + 3)(x + 1)(x - 1)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%20%2B%203%29%28x%20%2B%201%29%28x%20-%201%29)
We expand the last two factors using difference of two squares.
![f(x) = (x + 3)( {x}^{2} - 1)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%20%2B%203%29%28%20%7Bx%7D%5E%7B2%7D%20%20-%201%29)
![f(x) = x ( {x}^{2} - 1) + 3( {x}^{2} - 1)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%20%28%20%7Bx%7D%5E%7B2%7D%20%20-%201%29%20%2B%203%28%20%7Bx%7D%5E%7B2%7D%20%20-%201%29)
![f(x) = {x}^{3} - x+ 3 {x}^{2} -3](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7Bx%7D%5E%7B3%7D%20%20-%20x%2B%203%20%7Bx%7D%5E%7B2%7D%20%20-3)
![f(x) = {x}^{3} + 3 {x}^{2} - x -3](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7Bx%7D%5E%7B3%7D%20%20%2B%203%20%7Bx%7D%5E%7B2%7D%20%20-%20x%20-3)
This is the standard form because it is now in decreasing powers of x.
Answer:
R = sqrt[(IWL)^2/(E^2 - I^2)] or R = -sqrt[(IWL)^2/(E^2 - I^2)]
Step-by-step explanation:
Squaring both sides of equation:
I^2 = (ER)^2/(R^2 + (WL)^2)
<=>(ER)^2 = (I^2)*(R^2 + (WL)^2)
<=>(ER)^2 - (IR)^2 = (IWL)^2
<=> R^2(E^2 - I^2) = (IWL)^2
<=> R^2 = (IWL)^2/(E^2 - I^2)
<=> R = sqrt[(IWL)^2/(E^2 - I^2)] or R = -sqrt[(IWL)^2/(E^2 - I^2)]
Hope this helps!
Answer: 12
Step-by-step explanation: