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 (−∞, ∞)
.
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 .

Answer 1

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 \(x \geq 4000\).