mac1147_lecture12_1_c

# mac1147_lecture12_1_c - L12 Operations on Functions Graphs...

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119 L12 Operations on Functions; Graphs, Properties, and Library of Functions If f and g are two functions, then the sum fg + is a function defined by ( ) () x f x g x + =+ the difference is the function defined by ( ) x f x g x =− the product is the function defined by ( ) () () fgx f x g x =⋅ . The domain of each + , , or consists of all x that are in the domains of both f and g . The quotient f g is the function defined by ff x x gg x ⎛⎞ = ⎜⎟ ⎝⎠ . The domain of f g consists of all x that are in the domains of both f and g , for which () 0 gx .

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120 Example . Given 3 () 1 x fx x = + and ( ) ( 1) gx xx = + . Find each of the following and give the domain where it is appropriate. ( ) fg x = ( 1 ) fg f x g ⎛⎞ = ⎜⎟ ⎝⎠
121 Graph The graph of a relation in x and y is the set of all points in the xy -plane that correspond to the ordered pairs ( , ) x y . If a relation is a function, then for every x in the domain there is only one y , ( ) yf x = , in the range. With respect to the graph of a function it means that a vertical line x a = intersects the graph at one point (, () ) afa if a is in the domain of f , otherwise, x a = does not intersect the graph at all.

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mac1147_lecture12_1_c - L12 Operations on Functions Graphs...

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