Activity 3 - ( f ◦ g )( x ) = f ( g ( x )) ( f ◦ g )( x...

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Activity 3 Name 1.7 The Algebra of Functions We will cover 5 ways of combining functions. Consider the functions f ( x ) = x 2 + 2 and g ( x ) = x 3 - 2 x as examples. Operation Deﬁnition Example Addition ( f + g )( x ) = f ( x ) + g ( x ) ( f + g )( x ) = ( x 2 + 2) + ( x 3 - 2 x ) Subtraction ( f - g )( x ) = f ( x ) - g ( x ) ( f + g )( x ) = ( x 2 + 2) - ( x 3 - 2 x ) Multiplication ( fg )( x ) = f ( x ) g ( x ) ( fg )( x ) = ( x 2 + 2)( x 3 + 2 x ) Division ± f g ² ( x ) = f ( x ) g ( x ) ± f g ² ( x ) = x 2 +2 x 3 - 2 x Composition
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Unformatted text preview: ( f ◦ g )( x ) = f ( g ( x )) ( f ◦ g )( x ) = ( x 3-2 x ) 2 + 2 1. Given the function g ( t ) = 1 t + t 2 and h(t)=-2 t 3 , calculate ( g + h )( t ) = ( g-h )(1) = ( gh )( x ) = ( g h ) ( t ) = ± h g ² (-2) = ( g ◦ h )( t ) = ( h ◦ g )(1) =...
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This note was uploaded on 04/14/2008 for the course MATH 138 taught by Professor Hubbard during the Spring '08 term at Stephen F Austin State University.

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