Question

All computers are on sale for 10% off the original price. If x is the original price of the computer, then the function that represents the price after only a 10% discount is: P(x) = x - 0.1x P(x) = 0.9x The function that gives the price, C, if only a $150 coupon is used is: C(x) = x - 150 Choose the composition function that gives the final sale price after a 10% discount is followed by a $150 coupon. C(P(x)) = 0.9x – 150 P(C(x)) = 0.9x – 150 C(P(x)) = 1.9x – 150 P(C(x)) = 1.9x – 150

Answer 1

So the original price is "x".

the discounted price by 10% is P(x) = 0.9x.

the price minus a $150 coupon is C(x) = x - 150.

so, if you go to the store, the item is discounted by 10%, so you're really only getting out of your pocket 90% of that, or 0.9x, but!!! wait a minute!! you have a $150 coupon, and you can use that for the purchase, so you're really only getting out of  your pocket 0.9x - 150, namely the discounted by 10% and then the saving from the coupon.

C(   P(x)   ) = P(x) - 150

C(   P(x)   ) = 0.9x - 150

Answer 2

C(P(x)) = 0.9x – 150 is the correct answer.