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Real-World Composite Functions Composite functions are useful for real-world situations. EXAMPLE: Calculating the final cost of an item on sale First calculate the item's price. Then use the price to find the final cost, which includes the . The composite function for the final cost of the sale item is represented as The regular price of a dress shirt is $32.99, and it is on sale for 20% off. Sales tax is 6.3%. Write a function to represent the price of the shirt. f(x) = sale price of the shirt 100% - % = % Write a function to represent the final cost. g(x) = final cost of shirt *100% + % = % X Sale price, _( ), is calculated before tax, the 8(f(x)) = X) composition function can be written as _((x)). = 0.8504x = 0.8504 ( Substitute x = , and evaluate. = 28.05 When on sale for 20% off, the dress shirt costs $ including tax. Question Talmage received a coupon for $40 off the purchase of a used bike from a local bicycle shop. The bike he's buying costs $189, and the sales tax is 7.5%. Composite Function: Final Cost: O c(t(x)) = 1.075x -40 $160.18 O t(c(x)) = 1.075x-43 $ 163.18 OH(c(x)) = 0.675x $127.58