Respuesta :
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 [tex]f(x)=-2x-1[/tex] and [tex]g(x)=-3x+4[/tex]
We have to find the operation from the given options that results in the smallest coefficient on the x term .
Consider the given function [tex]f(x)=-2x-1[/tex] and [tex]g(x)=-3x+4[/tex]
b) Subtraction
That is f(x) - g(x)
[tex]f(x) -g(x)=-2x-1-(-3x+4)[/tex]
Apply plus - minus rule -(-a) = a , we have,
[tex]f(x)-g(x)=-2x-1+3x-4[/tex]
[tex]f(x)+g(x)=x-5[/tex]
Here, The coefficient of x is 1.
c) Multiplication
That is [tex]f(x)\cdot g(x)=(-2x-1)\cdot (-3x+4)[/tex]
[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
[tex]=\left(-2x\right)\left(-3x\right)+\left(-2x\right)\cdot \:4+\left(-1\right)\left(-3x\right)+\left(-1\right)\cdot \:4[/tex]
Simplify, we have,
[tex]=6x^2-5x-4[/tex]
Here, The coefficient of x is -5.
d) Addition
That is f(x) + g(x)
[tex]f(x)+g(x)=-2x-1+(-3x+4)[/tex]
Simplify, we have,
[tex]f(x)+g(x)=-2x-1-3x+4[/tex]
[tex]f(x)+g(x)=-5x+3[/tex]
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.
Answer:
a. two operations result in the same coefficient
Step-by-step explanation:
Here, the given functions,
f(x) = -2x - 1,
g(x) = -3x + 4,
Subtracting,
Case 1 : f(x) - g(x)
-2x - 1 + 3x - 4 = x - 5
Case 2 : g(x) - f(x)
3x - 4 + 2x + 1 = 5x - 3
Coefficient of x = 1 or 5
Multiplication :
f(x)* g(x) = (-2x - 1) (-3x + 4) = 6x² - 8x + 3x - 4 = 6x² - 5x - 4
Coefficient of x = -5
Addition :
f(x) + g(x) = -2x - 1 - 3x + 4 = -5x + 3
Coefficient of x = -5
Thus, the least coefficient of x = -5
And, two operation ( multiplication and addition ) operations result in the same coefficient
OPTION a is correct.
