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2.6_bzca5e - Section 2.6 Combinations of Functions...

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Section 2.6 Combinations of Functions: Composite Functions
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The Domain of a Function
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( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 3x+5 g(x)= x 4 5 x 4 5 0 5 1 0 5 0 1 0 x=5 x=-1 : - ,-1 1,5 5, x x x x x x Domain - - - - = - + = - = + = ∪ - 29 ( ) 2 5 2 5 0 2x 5 5 x 2 5 : , 2 h x x x Domain = - -
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( 29 2 ( ) 7 - , f x x x Domain = - ∞ ∞ Domains of Other Functions ( 29 ( ) 4 5 : , f x x Domain = - -∞ ∞ ( 29 3 ( ) : , f x x Domain = -∞ ∞
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Example Find the domain of the function 4x-1 f(x)= 3x+2
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Example Find the domain of the function f(x)= 4x-1
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The Algebra of Functions
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( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 f If the function can be g simplified, determine the domain before simplifying. Example; f(x)= x 4 and g(x)=x-2 f f x 2 in ; Domain of : ,2 2, g g 2 2 f 4 2 g 2 2 x x x x x x x - -∞ - + - = = = + ÷ - -
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The domain of f+g is the set of all real numbers that are common to the domain of f and the domain of g. Thus we must find the domains of f and g before finding their intersection. Suppose ( ) x+3 a f x = nd g(x)= x-2 then (f+g)(x)= x+3 2 Now for their domains.
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