Question

juliana, an architect, buys a drawing table on sale for 20% off. she also gets a 15% store membership discount on the sale price. use composition of functions to determine the expression for the final cost of a drawing table. let (x) be the initial price of the drawing table.

(0.32x)
(0.35x)
(0.65x)
(0.68x)

Explanation:

⚡ Using what you learned: Evaluating Composite Functions

Step 1: Define the sale price function

Let \( x \) be the initial price of the drawing table.

A \( 20\% \) discount means paying \( 80\% \) of the original price:

$$ s(x) = x - 0.20x = 0.80x $$

Step 2: Define the membership discount function

A \( 15\% \) discount on an input price \( y \) means paying \( 85\% \) of that price:

$$ m(y) = y - 0.15y = 0.85y $$

Step 3: Compose the functions

Apply the membership discount to the sale price by finding \( (m \circ s)(x) \):

$$ m(s(x)) = 0.85(0.80x) $$

$$ m(s(x)) = 0.68x $$

Answer:

\( 0.68x \)