Question

Given the function f(x)=-2x-1 and g(x)=-3x 4 which operation results in the smallest coefficient on the x term?

a. two operations result in the same coefficient
b. subtraction
c. multiplication
d. addition

Answer 1

a. two operations result in the same coefficient

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.

Answer 2

Option (a) is correct.

The smallest coefficient on x - terms will be obtained by addition and multiplication of two given functions.

Explanation:

Given: The function
`f(x)=-2x-1` and
`g(x)=-3x+4`

We have to find the operation from the given options that results in the smallest coefficient on the x term .

Consider the given function
`f(x)=-2x-1` and
`g(x)=-3x+4`

b) Subtraction

That is f(x) - g(x)

`f(x) -g(x)=-2x-1-(-3x+4)`

Apply plus - minus rule -(-a) = a , we have,

`f(x)-g(x)=-2x-1+3x-4`

`f(x)+g(x)=x-5`

Here, The coefficient of x is 1.

c) Multiplication

That is
`f(x)\cdot g(x)=(-2x-1)\cdot (-3x+4)`

`\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd`

`=\left(-2x\right)\left(-3x\right)+\left(-2x\right)\cdot \:4+\left(-1\right)\left(-3x\right)+\left(-1\right)\cdot \:4`

Simplify, we have,

`=6x^2-5x-4`

Here, The coefficient of x is -5.

d) Addition

That is f(x) + g(x)

`f(x)+g(x)=-2x-1+(-3x+4)`

Simplify, we have,

`f(x)+g(x)=-2x-1-3x+4`

`f(x)+g(x)=-5x+3`

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.