M1410108 - (Section 1.8: Combining Functions) 1.92 SECTION...

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(Section 1.8: Combining Functions) 1.92 SECTION 1.8: COMBINING FUNCTIONS PART A: ARITHMETIC COMBINATIONS Let f and g be functions. If their domains overlap, then the overlap is the domain of the following functions, with one exception (*): f + g , where f + g ( ) x ( ) = f x ( ) + g x ( ) f g , where f g ( ) x ( ) = f x ( ) g x ( ) fg , where fg ( ) x ( ) = f x ( ) g x ( ) f g , where f g x ( ) = f x ( ) g x ( ) (*) Values of x that make g x ( ) = 0 must be excluded from the domain of f g . Example If f x ( ) = 4 x and g x ( ) = x + 1 x , find f g ( ) x ( ) and the domain of f g . Solution f g ( ) x ( ) = f x ( ) g x ( ) = 4 x x + 1 x Warning : Remember the grouping symbols around g x ( ) . = 4 x x 1 x = 3 x 1 x We omit 0 from the domain of g and, therefore, the domain of f g . The domain of f g is: −∞ ,0 ( ) 0, ( ) .
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1.93 Example If f x ( ) = 1 and g x ( ) = x x 2 , find f g x ( ) and the domain of f g . Solution f g x ( ) = f x ( ) g x ( ) = 1 x x 2 = x 2 x g x ( ) = 0 when x = 0 , and g x ( ) is undefined when x = 2 , so we must exclude both 0 and 2 from the domain of f g .
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M1410108 - (Section 1.8: Combining Functions) 1.92 SECTION...

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