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
Answer:
The final price of the computer after both discounts is T(x) = 0.9x - 150
Solution:
We have been given that 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
We need to choose the composition function that gives the final sale price after a 10% discount is followed by a $150 coupon.
So, we have to formulate a function to combine both the discounts.
The price after 10% discount is 0.9x and the price after $150 coupon is x-150.
So, the composite function that gives the final sale price after 10% discount followed by $150 is given as follows:
Let the final price be denoted as T(x)
Therefore,
T(x) = original price - 10% discount - $150 coupon
T(x) = x - 10% of x -150
T(x) = x - 0.1x - 150
T(x) = 0.9x -150
Hence the final price of the computer after both discounts is T(x) = 0.9x-150