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, which of the following represents the final price of a gaming system with the discount and taxes applied?

c(p) + p(g) = 1.92g
c[p(g)] = 0.896g
g[c(p)] = 1.92p
c(p) ⋅ p(g) = 0.896pg

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, which of the following represents the final price of a gaming system with the discount and taxes applied?

 c(p) + p(g) = 1.92g
 c[p(g)] = 0.896g
 g[c(p)] = 1.92p
 c(p) ⋅ p(g) = 0.896pg

anonymous · Answer

@freckles can you help me with this one?

freckles · Answer

just find c(p(g))

freckles · Answer

it is just another composition function question

anonymous · Answer

So the answer is B?

freckles · Answer

by the way this is the way I figured it out...
we are given let's say g 
g is on sale for 20$ off the original price
so that is g - g(.2)
which is g(1-.2)=g(.8)
Ok now this is the price of the game .8g before going into taxes
taxes is 12%
you have to paid for the game plus taxes
so (.8g)+(.8g)*.12
factoring (.8g)(1+.12)=.8g(1.12)
and then you can do .8 * 1.12 to simplify further

freckles · Answer

and yes that is the only choice that matches

anonymous · Answer

I understand now