A company sells cell phones and watches. The function f(x)=8x+10

Question

represents the number of cell phones in thousands the company sells after x years. The function f(x)=25x+500
represents the number of watches in thousands the company sells after x years. What function represents how many more cell phones the company sells after x years than watches? What is the domain?(1 point)
Responses

(f−g)(x)=8x+25x+510
and the domain (f−g)(x)
is x≥0
.
open paren f minus g close paren of x is equal to 8 to the x th power plus 25 x plus 510 and the domain open paren f minus g close paren of x is x is greater than or equal to 0 .

(f−g)(x)=8x−25x−490
and the domain (f−g)(x)
is x≥0
.
open paren f minus g close paren of x is equal to 8 to the x th power minus 25 x minus 490 and the domain open paren f minus g close paren of x is x is greater than or equal to 0 .

(f−g)(x)=8x+25x+510
and the domain (f−g)(x)
is (−∞,∞)
.
open paren f minus g close paren of x is equal to 8 to the x th power plus 25 x plus 510 and the domain open paren f minus g close paren of x is open paren negative infinity comma infinity close paren .

(f−g)(x)=8x−25x−490
and the domain (f−g)(x)
is (−∞,∞)
.
open paren f minus g close paren of x is equal to 8 to the x th power minus 25 x minus 490 and the domain open paren f minus g close paren of x is open paren negative infinity comma infinity close paren .

Answer 1

To find the function that represents how many more cell phones the company sells than watches, we will define the two functions based on the information given:

1. The number of cell phones sold after \( x \) years is represented by the function \( f(x) = 8x + 10 \).
2. The number of watches sold after \( x \) years is represented by the function \( g(x) = 25x + 500 \).

To find how many more cell phones the company sells than watches, we calculate \( f(x) - g(x) \):

\[ (f - g)(x) = f(x) - g(x) = (8x + 10) - (25x + 500) \]

Now, simplifying this expression:

\[ (f - g)(x) = 8x + 10 - 25x - 500 \] \[ = 8x - 25x + 10 - 500 \] \[ = -17x - 490 \]

So we have:

\[ (f - g)(x) = -17x - 490 \]

Now, regarding the domain of the function \( (f - g)(x) \), since both the functions \( f(x) \) and \( g(x) \) are linear and defined for all real numbers, the domain of \( (f - g)(x) \) is:

\[ x \geq 0 \]

Thus, the correct response is:

\[ (f - g)(x) = -17x - 490 \text{ and the domain } (f - g)(x) \text{ is } x \geq 0. \]

None of the provided responses match this conclusion. Please double-check the provided options.