composite functions - MAC1105 Composition of Functions Many...

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MAC1105: Composition of Functions Many real world events involve a multi-step sequence of events in which the result of each step determines the next step. Suppose that you want to paint your house, but your paint budget is limited. Your budget determines the amount of paint that you can buy and the amount of paint you buy determines the amount of wall space you can paint. Ultimately, your budget determines the amount of wall space you can paint. In functional language, the amount of paint you can buy is a function of your budget and the amount of wall space you can paint is a function of the amount of paint you buy. The process of combining these two functions together to represent the amount of wall space you can paint as a function of your budget is called composition . Example: You have $50 in your budget to spend on paint. Paint costs $8 per gallon, and each gallon can cover 200 square feet of wall space. a. Construct a formula that expresses the number of gallons of paint G that can be bought with x dollars.
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