The formula F = ma represents the force on an object in newtons with a mass of m kilograms and an acceleration of a meters per second. The mass of an object is given by the functionf(x)=|5−x|

Question

. The acceleration of the object is given by the function g(x)=2x+1
. What function represents the force on the object? What is the domain?(1 point)
Responses

(f+g)(x)=|5−x|+2x+1
and the domain is (−∞,∞)
.
open paren f plus g close paren of x is equal to start absolute value 5 minus x end absolute value plus 2 to the x th power plus 1 and the domain is open paren negative infinity comma infinity close paren .

(f⋅g)(x)=2x|5−x|+|5−x|
and the domain is (−∞,∞)
.
open paren f times g close paren of x is equal to 2 to the x th power divides 5 minus x divides plus start absolute value 5 minus x end absolute value and the domain is open paren negative infinity comma infinity close paren .

(f+g)(x)=|5−x|+2x+1
and the domain is x≠5
.
open paren f plus g close paren of x is equal to start absolute value 5 minus x end absolute value plus 2 to the x th power plus 1 and the domain is x is not equal to 5 .

(f⋅g)(x)=2x|5−x|+|5−x|
and the domain is x≠5
.

Answer 1

To find the function that represents the force on the object using the formula \( F = ma \), we need to substitute the given functions for mass \( m \) and acceleration \( a \):

• Mass of the object: \( f(x) = |5 - x| \)
• Acceleration of the object: \( g(x) = 2x + 1 \)

The force \( F \) can be represented by the function:

\[ F(x) = f(x) \cdot g(x) = |5 - x| \cdot (2x + 1) \]

Thus, the force function is:

\[ F(x) = |5 - x| (2x + 1) \]

Next, we need to determine the domain of this function. The absolute value function \( |5 - x| \) is defined for all real numbers \( x \), and since \( g(x) = 2x + 1 \) is also defined for all real numbers, the product \( |5 - x|(2x + 1) \) also has no restrictions based on the function structure.

Therefore, the domain of \( F(x) \) is:

\[ (-\infty, \infty) \]

Now, looking at your options, the correct answer is:

\[ F(x) = |5 - x|(2x + 1) \text{ and the domain is } (-\infty, \infty). \]

However, since none of the original response options provided match this notation exactly, we should conclude that the correct representation of force is \( (f \cdot g)(x) = |5 - x|(2x + 1) \) with the domain \( (-\infty, \infty) \).