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Chapter 9 – Combination of Functions

Chapter 9 – Combination of Functions. Aiswarya, Amanpreet, and Liban. 9.1- Exploring Combinations of Functions. The characteristic of the function that are combined affect the properties and the characteristic of the resulting function such as * Adding (f + g) (x) * Subtracting (f - g) (x)

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Chapter 9 – Combination of Functions

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  1. Chapter 9 – Combination of Functions Aiswarya, Amanpreet, and Liban

  2. 9.1- Exploring Combinations of Functions • The characteristic of the function that are combined affect the properties and the characteristic of the resulting function such as * Adding (f + g) (x) * Subtracting (f - g) (x) * Dividing (f / g) (x) * Multiplying (f x g) (x)

  3. 9.2- Combining Two Functions: Sums and Difference • When two functions are combined to form (f + g) (x) than the graph of f(x) and g(x) could be used to graph the (f + g) (x). This rule is also applicable to (f - g) (x) • The domain of f + g or f – g is the intersection of the domains of f and g. This means that the functions f +g and f-g are only defined where the domains of both f and g overlap.

  4. 9.3- Combining Two Functions: Products • When two functions are combined to form (f x g) (x) than the graph of f(x) and g(x) could be used to graph the (f x g) (x). • (f x g) (x) is the product of f(x) x g(x) • The domain of f x g is the intersection of the domains of f and g • If f(x) = ‘+’ or ‘-‘ 1 then (f x g) (x) = ‘+’ or ‘-‘ g. Same goes for g(x) = ‘+’ or ‘-‘ 1 then (f x g) (x) = ‘+’ or ‘-‘f

  5. 9.4- Exploring Quotients of Functions • When two functions are combined to form (f / g) (x) than the graph of f(x) and g(x) could be used to graph the (f / g) (x). • (f / g) (x) is the quotient of f(x) and g(x) • f/g will be defined for all the x values that are in the intersection of the domains of f and g, expect in the case of g(x) = 0. If the domain of f is C and the domain of g is D, then the domain of f/g is {x€ R/x€ CΠ D, g(x) ≠0} • If f(x) = 0 when g(x) ≠ 0, then (f/g) (x) = 0

  6. 9.5-Composition of Functions • Composition of f with g is denoted by (f 0 g) (x), and g with f is denoted by (g 0 f) (x). • A point in f 0 g exists where an element in the range of g is also in the domain of f. • f 0 g exists only when the range of g overlaps the domain of f. • If both f and f^-1 are functions, then (f ^-1 0 f)=x for all x in the domain of f, and (f 0 f ^-1)(x)=x for all x in the domain of f^-1.

  7. 9.7-Modelling with Functions • Often necessary to restrict the domain of a mathematical model to represent a realistic situation. • For a problem, use a method that describes and answers the problem thoroughly.

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