The function f(x)=0.04x

Question

represents the amount Sally earns in commission where x is the amount of sales in dollars. The function g(x)=x−4,000
represents the amount of sales on which Sally gets paid commission. What is (f∘g)(x)
and what does it mean? What is the domain?(1 point)
Responses

(f∘g)(x)=0.04x−160
represents the amount Sally earns in commission. The domain is x≥0
.
open paren f circ g close paren times x is equal to 0 point 0 4 x minus 160 represents the amount Sally earns in commission. The domain is x is greater than or equal to 0 .

(f∘g)(x)=0.04x−4,000
represents the amount Sally earns in salary and commission. The domain is x≥0
.
open paren f circ g close paren times x is equal to 0 point 0 4 x minus 4 comma 000 represents the amount Sally earns in salary and commission. The domain is x is greater than or equal to 0 .

(f∘g)(x)=0.04x−4,000
represents the amount Sally earns in salary and commission. The domain is (−∞, ∞)
.
open paren f circ g close paren times x is equal to 0 point 0 4 x minus 4 comma 000 represents the amount Sally earns in salary and commission. The domain is open paren negative infinity comma infinity close paren .

(f∘g)(x)=0.04x−160
represents the amount Sally earns in commission. The domain is (−∞, ∞)
.

Answer 1

To find \((f \circ g)(x)\), we first need to substitute \(g(x)\) into \(f(x)\).

1. Finding \((f \circ g)(x)\):

   The function \(g(x) = x - 4,000\). Now substitute \(g(x)\) into \(f(x)\):

   \[ f(g(x)) = f(x - 4,000) = 0.04(x - 4,000) = 0.04x - 0.04 \cdot 4,000 \] \[ f(g(x)) = 0.04x - 160 \]

So, we have \((f \circ g)(x) = 0.04x - 160\).

2. Meaning:

   This means that \((f \circ g)(x)\) represents the amount Sally earns in commission based on her total sales, where \(x\) is the total sales amount in dollars. The term \(-160\) represents the threshold amount that needs to be surpassed (the $4,000 in sales) before Sally starts earning commission from her sales.

3. Domain:

   Since \(g(x)\) gives the amount of sales on which Sally earns commission, it requires \(g(x) \geq 0\).

   Therefore, we require:

   \[ x - 4,000 \geq 0 \Rightarrow x \geq 4,000 \]

Thus, the domain of \((f \circ g)(x)\) is \(x \geq 4,000\).

Correct response:

\((f \circ g)(x) = 0.04x - 160\) represents the amount Sally earns in commission. The domain is \(x \geq 4,000\).