Answer:
Option (a) is correct.
The smallest coefficient on x - terms will be obtained by addition and multiplication of two given functions.
Step-by-step explanation:
Given: The function
and ![g(x)=-3x+4](https://tex.z-dn.net/?f=g%28x%29%3D-3x%2B4)
We have to find the operation from the given options that results in the smallest coefficient on the x term .
Consider the given function
and ![g(x)=-3x+4](https://tex.z-dn.net/?f=g%28x%29%3D-3x%2B4)
b) Subtraction
That is f(x) - g(x)
![f(x) -g(x)=-2x-1-(-3x+4)](https://tex.z-dn.net/?f=f%28x%29%20-g%28x%29%3D-2x-1-%28-3x%2B4%29)
Apply plus - minus rule -(-a) = a , we have,
![f(x)-g(x)=-2x-1+3x-4](https://tex.z-dn.net/?f=f%28x%29-g%28x%29%3D-2x-1%2B3x-4)
![f(x)+g(x)=x-5](https://tex.z-dn.net/?f=f%28x%29%2Bg%28x%29%3Dx-5)
Here, The coefficient of x is 1.
c) Multiplication
That is
![\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3AFOIL%5C%3Amethod%7D%3A%5Cquad%20%5Cleft%28a%2Bb%5Cright%29%5Cleft%28c%2Bd%5Cright%29%3Dac%2Bad%2Bbc%2Bbd)
![=\left(-2x\right)\left(-3x\right)+\left(-2x\right)\cdot \:4+\left(-1\right)\left(-3x\right)+\left(-1\right)\cdot \:4](https://tex.z-dn.net/?f=%3D%5Cleft%28-2x%5Cright%29%5Cleft%28-3x%5Cright%29%2B%5Cleft%28-2x%5Cright%29%5Ccdot%20%5C%3A4%2B%5Cleft%28-1%5Cright%29%5Cleft%28-3x%5Cright%29%2B%5Cleft%28-1%5Cright%29%5Ccdot%20%5C%3A4)
Simplify, we have,
![=6x^2-5x-4](https://tex.z-dn.net/?f=%3D6x%5E2-5x-4)
Here, The coefficient of x is -5.
d) Addition
That is f(x) + g(x)
![f(x)+g(x)=-2x-1+(-3x+4)](https://tex.z-dn.net/?f=f%28x%29%2Bg%28x%29%3D-2x-1%2B%28-3x%2B4%29)
Simplify, we have,
![f(x)+g(x)=-2x-1-3x+4](https://tex.z-dn.net/?f=f%28x%29%2Bg%28x%29%3D-2x-1-3x%2B4)
![f(x)+g(x)=-5x+3](https://tex.z-dn.net/?f=f%28x%29%2Bg%28x%29%3D-5x%2B3)
Here, The coefficient of x is -5.
a) two operations result in the same coefficient.
When we add or multiply the two given function, we obtain the same coefficient of x that is -5
Hence, The smallest coefficient on x - terms will be obtained by addition and multiplication of two given functions.