Respuesta :

mixter17

Hello!

The answer is:

The fourth option,

[tex](f-g)(x)=11x[/tex]

Why?

To solve the problem, we must remember the following property of the functions:

Subtraction of functions:

We have that,

[tex](f-g)(x)=f(x)-g(x)[/tex]

We are given the functions:

[tex]f(x)=4x+3[/tex]

and

[tex]g(x)=3-7x[/tex]

So, calculating we have:

[tex](f-g)(x)=f(x)-g(x)[/tex]

[tex](f-g)(x)=(4x+3)-(3-7x)[/tex]

[tex](f-g)(x)=4x+3-3+7x[/tex]

[tex](f-g)(x)=4x+7x+3-3=11x[/tex]

Hence, the answer is the fourth option,

[tex](f-g)(x)=11x[/tex]

Have a nice day!

sylvain96

Answer:

(D) (f-g)(x) = 11x

Step-by-step explanation:

You have:

f(x) = 4x + 3

g(x) = 3 - 7x

You want to do f(x) - g(x)... you simply do the operation on their definition...

f(x) - g(x) = 4x + 3 - (3 - 7x) = 4x + 3 - 3 + 7x = 11 x + 0

So, (f-g)(x) = 11x

You can verify it by placing a value for x in both equations.  Let's take x = 3

f(x) = 4x + 3 = 4(3) + 3 = 15

g(x) = 3 - 7x = 3 - 7(3) = -18

f(x) - g(x) = 15 - -18 = 33

(f - g)(x) = 11x = 11 (3) = 33

Yes, (f(x) - g(x)) = (f - g)(x) = 33

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