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.
