Question

Gaming systems are on sale for 20% off the original price (g), which can be expressed with the function p(g) = 0.8g. Local taxes are an additional 12% of the discounted price (p), which can be expressed with the function c(p) = 1.12p. Using this information, choose the best representation of the final price of a gaming system with the discount and taxes applied.
A.) c(p) + p(g) = 1.92g
B.) c[p(g)] = 0.896g
C.) g[c(p)] = 1.92p
D.) c(p) ⋅ p(g) = 0.896pg

Answer 1

Answer:

B. $c[p(g)]=0.896g$

Step-by-step explanation:  

We have been given that gaming systems are on sale for 20% off the original price (g), which can be expressed with the function p(g) = 0.8g.

$\text{The price of gaming system after discount}=g-\frac{20}{100}g$

$\text{The price of gaming system after discount}=g-0.20g$

$\text{The price of gaming system after discount}=0.80g$  

We are also given that local taxes are an additional 12% of the discounted price, so final price of gaming system will be 0.8g plus 12% of 0.8g.

$\text{Price of the gaming system after sales tax}=0.8g+(\frac{12}{100}\times 0.8g)$  

$\text{Price of the gaming system after sales tax}=0.8g+(0.12\times 0.8g)$  

Upon factoring out 0.8 we will get,

$\text{Price of the gaming system after sales tax}=0.8g(1+0.12)$  

$\text{Price of the gaming system after sales tax}=0.8g(1.12)$  

We can see that this is a composite function as:

$p(g)=0.8g$

$c(p)=1.12p$  

Upon substituting p's value in 2nd function we will get,

$c[p(g)]=1.12*0.8g$

$c[p(g)]=0.896g$

Therefore, the composite function $c[p(g)]=0.896g$ represents the final  price of a gaming system with the discount and taxes applied and option B is the correct choice.

Answer 2

"c[p(g)] = 0.896g" is the one among the following choices given in the question that is the best representation of the final price of a gaming system with the discount and taxes applied. The correct option among all the options that are given in the question is the second option or option "B". I hope it helps you.