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Published byElmer Jordan Modified over 9 years ago
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Composite Functions Example 1:Given functions f(x) = x 2 – 3x and g(x) = 2x + 1, find f g. The notation "f g" means f (g(x)). In other words, replace x in function f with 2x + 1 (the g function). f (x ) = (x) 2 – 3(x)
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Composite Functions Example 1:Given functions f(x) = x 2 – 3x and g(x) = 2x + 1, find f g. The notation "f g" means f (g(x)). In other words, replace x in function f with 2x + 1 (the g function). f (x ) = ( ) 2 – 3( ) f g = f (g(x)) = (2x + 1) 2 – 3(2x + 1) f g = 4x 2 + 4x + 1 – 6x – 3 f g = 4x 2 – 2x – 2
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Composite Functions Example 2:Given functions and find f g and state its domain. x x Simplify the complex fraction by multiplying the numerator and denominator by x + 1.
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Composite Functions At first glance it might appear that the domain of f g is the set of all real numbers except - 1.5.
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Composite Functions Since the g function is not defined for x = - 1, neither is the f g function. However, remember that the g function, replaced x in the f function. Therefore, the domain of f g is: ( - , - 1.5 ) ( - 1.5, - 1 ) ( - 1, ).
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Composite Functions Try:Given functions and find f g and state its domain. Its domain is: [ - 5, ). The composite function, f g = x.
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Composite Functions
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