Question

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+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+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 .

(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 .
Skip to navigation

Answer 1

To find the function that represents how many more cell phones the company sells after \(x\) years than watches, we need to compute the difference between the two functions for cell phones \( f(x) = 8x + 10 \) and watches \( g(x) = 25x + 500 \).

The difference \( (f - g)(x) \) is calculated as follows:

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

Substituting the functions:

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

Now, simplifying:

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

So the function representing how many more cell phones the company sells after \(x\) years than watches is:

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

Next, regarding the domain: since \(x\) represents the number of years and it cannot be negative, the domain is \( x \geq 0 \).

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

Therefore, the correct response is: \((f-g)(x)=-17x-490\) and the domain \((f-g)(x)\) is \(x \geq 0\).