I Need to find the Function Operations
1 answer:
Answer:
1) ![(f+g)(x)=2x^2+3x-6](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D2x%5E2%2B3x-6)
2) ![(f-g)(x)=2x^2+x](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3D2x%5E2%2Bx)
3) ![(f \cdot g)(x)=2x^3-4x^2-9x+9](https://tex.z-dn.net/?f=%28f%20%5Ccdot%20g%29%28x%29%3D2x%5E3-4x%5E2-9x%2B9)
Step-by-step explanation:
So we have the two functions:
![f(x)=2x^2+2x-3\text{ and } g(x)=x-3](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E2%2B2x-3%5Ctext%7B%20and%20%7D%20g%28x%29%3Dx-3)
And we want to find (f+g)(x), (f-g)(x), and (f*g)(x).
1)
(f+g)(x) is the same to f(x)+g(x). Substitute:
![(f+g)(x)=f(x)+g(x)\\=(2x^2+2x-3)+(x-3)](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3Df%28x%29%2Bg%28x%29%5C%5C%3D%282x%5E2%2B2x-3%29%2B%28x-3%29)
Combine like terms:
![=(2x^2)+(2x+x)+(-3-3)](https://tex.z-dn.net/?f=%3D%282x%5E2%29%2B%282x%2Bx%29%2B%28-3-3%29)
Add:
![=2x^2+3x-6](https://tex.z-dn.net/?f=%3D2x%5E2%2B3x-6)
So:
![(f+g)(x)=2x^2+3x-6](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D2x%5E2%2B3x-6)
2)
(f-g)(x) is the same to f(x)-g(x). So:
![(f-g)(x)=f(x)-g(x)\\=(2x^2+2x-3)-(x-3)](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3Df%28x%29-g%28x%29%5C%5C%3D%282x%5E2%2B2x-3%29-%28x-3%29)
Distribute:
![=(2x^2+2x-3)+(-x+3)](https://tex.z-dn.net/?f=%3D%282x%5E2%2B2x-3%29%2B%28-x%2B3%29)
Combine like terms:
![=(2x^2)+(2x-x)+(-3+3)](https://tex.z-dn.net/?f=%3D%282x%5E2%29%2B%282x-x%29%2B%28-3%2B3%29)
Simplify:
![=2x^2+x](https://tex.z-dn.net/?f=%3D2x%5E2%2Bx)
So:
![(f-g)(x)=2x^2+x](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3D2x%5E2%2Bx)
3)
(f*g)(x) is the same to f(x)*g(x). Thus:
![(f\cdot g)(x)=f(x)\cdot g(x)\\=(2x^2+2x-3)(x-3)](https://tex.z-dn.net/?f=%28f%5Ccdot%20g%29%28x%29%3Df%28x%29%5Ccdot%20g%28x%29%5C%5C%3D%282x%5E2%2B2x-3%29%28x-3%29)
Distribute:
![=(2x^2+2x-3)(x)+(2x^2+2x-3)(-3)](https://tex.z-dn.net/?f=%3D%282x%5E2%2B2x-3%29%28x%29%2B%282x%5E2%2B2x-3%29%28-3%29)
Distribute:
![=(2x^3+2x^2-3x)+(-6x^2-6x+9)](https://tex.z-dn.net/?f=%3D%282x%5E3%2B2x%5E2-3x%29%2B%28-6x%5E2-6x%2B9%29)
Combine like terms:
![=(2x^3)+(2x^2-6x^2)+(-3x-6x)+(9)](https://tex.z-dn.net/?f=%3D%282x%5E3%29%2B%282x%5E2-6x%5E2%29%2B%28-3x-6x%29%2B%289%29)
Simplify:
![=2x^3-4x^2-9x+9](https://tex.z-dn.net/?f=%3D2x%5E3-4x%5E2-9x%2B9)
So:
![(f \cdot g)(x)=2x^3-4x^2-9x+9](https://tex.z-dn.net/?f=%28f%20%5Ccdot%20g%29%28x%29%3D2x%5E3-4x%5E2-9x%2B9)
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Step-by-step explanation: