Section 2.7 Combining Functions Objectives: To add, subtract, multiply and divide functions. Composition of functions.

Two functions f and g can be combined to form new functions f + g, f – g, fg, f/g in a manner similar to the way we add, subtract, multiply, and divide real numbers.

Let f and g be functions with domains A and B. Then, the functions f + g, f – g, fg, and f/g are defined as follows.

Ex 1. Let and (a)Find the functions f + g, f – g, fg, and f/g and their domains. (b)Find (f + g)(-1), (f – g)(3), (fg)(4), and (f/g)(2).

Class Work 1. Let and a.) Find the function and its domain. b.) Find

Given two functions f and g, the composite function f ◦ g (also called the composition of f and g) is defined by: (f ◦ g)(x) = f [g(x)]

Ex 2. Let f(x) = x 2 and g(x) = x – 3 (a)Find the functions f ◦ g and g ◦ f and their domains. (b)Find (f ◦ g)(5) and (g ◦ f )(7).

Class Work 2. Let f(x) = x 2 and g(x) = x + 5. (a)Find the functions f ◦ g and g ◦ f and their domains. (b)Find (f ◦ g)(-2) and (g ◦ f )(4).

Ex 3. If f(x) = and g(x) =, find the following functions and their domains. (a) f ◦ g (b) g ◦ f (c) f ◦ f (d) g ◦ g

Class Work 3. Let. Find: a) b) c)

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