Question
The function f(x)=0.04x
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 (−∞, ∞)
.
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 open paren negative infinity comma infinity close paren .
(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−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−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 .
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 (−∞, ∞)
.
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 open paren negative infinity comma infinity close paren .
(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−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−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 .
Answers
GPT-4o mini
To find \((f \circ g)(x)\), we need to substitute the function \(g(x)\) into the function \(f(x)\).
1. We have:
- \(f(x) = 0.04x\)
- \(g(x) = x - 4000\)
2. Now, calculate \((f \circ g)(x)\):
\[
(f \circ g)(x) = f(g(x)) = f(x - 4000)
\]
\[
= 0.04(x - 4000)
\]
\[
= 0.04x - 0.04 \cdot 4000
\]
\[
= 0.04x - 160
\]
Thus, \((f \circ g)(x) = 0.04x - 160\).
### Interpretation
This expression \((f \circ g)(x) = 0.04x - 160\) represents the amount Sally earns in commission, after accounting for the fact that she does not earn commission on the first $4,000 in sales. The additional term \(-160\) reflects a deduction due to the $4,000 threshold generally indicating that she does not receive commission on sales below that level.
### Domain
The domain of \((f \circ g)(x)\) is determined by the function \(g(x) = x - 4000\) since sales cannot be negative. Therefore, for Sally to earn a commission, her sales \(x\) should be at least $4,000, meaning:
\[
x \geq 4000
\]
So, the domain can be represented as \(x \geq 4000\).
### Conclusion
The correct response is:
\((f \circ g)(x) = 0.04x - 160\) represents the amount Sally earns in commission. The domain is \(x \geq 4000\).
1. We have:
- \(f(x) = 0.04x\)
- \(g(x) = x - 4000\)
2. Now, calculate \((f \circ g)(x)\):
\[
(f \circ g)(x) = f(g(x)) = f(x - 4000)
\]
\[
= 0.04(x - 4000)
\]
\[
= 0.04x - 0.04 \cdot 4000
\]
\[
= 0.04x - 160
\]
Thus, \((f \circ g)(x) = 0.04x - 160\).
### Interpretation
This expression \((f \circ g)(x) = 0.04x - 160\) represents the amount Sally earns in commission, after accounting for the fact that she does not earn commission on the first $4,000 in sales. The additional term \(-160\) reflects a deduction due to the $4,000 threshold generally indicating that she does not receive commission on sales below that level.
### Domain
The domain of \((f \circ g)(x)\) is determined by the function \(g(x) = x - 4000\) since sales cannot be negative. Therefore, for Sally to earn a commission, her sales \(x\) should be at least $4,000, meaning:
\[
x \geq 4000
\]
So, the domain can be represented as \(x \geq 4000\).
### Conclusion
The correct response is:
\((f \circ g)(x) = 0.04x - 160\) represents the amount Sally earns in commission. The domain is \(x \geq 4000\).