Question

A company sells cell phones and watches. The function f(x)=8x+10
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−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+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 (−∞,∞)
.
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 determine the function that represents how many more cell phones the company sells after \( x \) years than watches, we need to find the difference between the number of cell phones sold and the number of watches sold.

Given functions:
- \( f(x) = 8x + 10 \) (cell phones sold in thousands)
- \( g(x) = 25x + 500 \) (watches sold in thousands)

The function representing how many more cell phones are sold than watches is given by:
\[
(f - g)(x) = f(x) - g(x)
\]
Substituting the functions:
\[
(f - g)(x) = (8x + 10) - (25x + 500)
\]
Now, simplify the difference:
\[
(f - g)(x) = 8x + 10 - 25x - 500
\]
\[
= 8x - 25x + 10 - 500
\]
\[
= -17x - 490
\]

Thus, the function that represents how many more cell phones the company sells than watches is:
\[
(f - g)(x) = -17x - 490
\]

The domain is based on the context of x representing years, so \( x \) should be greater than or equal to 0:
\[
\text{Domain: } x \geq 0
\]

In conclusion, 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 response options match the final derived function, so please check again or confirm the correct values.