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)=|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 (−∞,∞)
.
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)=2x|5−x|+|5−x|
and the domain is x≠5
.
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 x is not equal to 5 .

Answer 1

To find the force on the object, we need to use the formula \( F = ma \) where \( m \) is the mass given by the function \( f(x) = |5 - x| \) and \( a \) is the acceleration given by the function \( g(x) = 2x + 1 \).

Thus, the function representing the force \( F(x) \) is calculated as follows:

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

This can be rewritten as:

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

Now, let's look at the domain of this expression. The absolute value function \( |5 - x| \) is defined for all real numbers, and the linear function \( 2x + 1 \) is also defined for all real numbers. Therefore, the overall domain of \( F(x) \) is:

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

Putting this all together, the function representing the force on the object is:

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

And the domain is:

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

So the correct response is:

\((f \cdot g)(x) = |5 - x|(2x + 1)\) and the domain is \((- \infty, \infty)\).