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 (−∞,∞)
.
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 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−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 .

(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 .

Answer 1

To find the function that represents how many more cell phones the company sells after \( x \) years than watches, we need to formulate the difference between the two functions that represent the number of cell phones and the number of watches.

1. Function for cell phones:
   \( f(x) = 8x + 10 \) (in thousands)

2. Function for watches:
   \( g(x) = 25x + 500 \) (in thousands)

The formula that shows how many more cell phones the company sells than watches is given by:
\[ (f - g)(x) = f(x) - g(x) \] Substituting the functions into this equation gives:
\[ (f - g)(x) = (8x + 10) - (25x + 500) \]

Now, we distribute the negative sign:
\[ (f - g)(x) = 8x + 10 - 25x - 500 \]

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

Now we have the function representing how many more cell phones are sold than watches:
\[ (f - g)(x) = -17x - 490 \]

Domain:
Since \( x \) represents the number of years, it can be any non-negative number. Therefore, the domain is:
\[ x \geq 0 \]

So, the final answer is: \[ (f - g)(x) = -17x - 490 \quad \text{and the domain is } x \geq 0. \]