Mth141S26n - Sec 2.6 Operations and Composition We can...

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Sec. 2.6 – Operations and Composition We can combine functions using the operations of addition, subtraction, multiplication, and division. Addition of functions : ( )( ) ( ) ( ) f g x f x g x + = + Subtraction of functions : ( )( ) ( ) ( ) f g x f x g x - = - Multiplication of functions : ( )( ) ( ) ( ) f g x f x g x = Division of functions : ( / )( ) ( ) / ( ) f g x f x g x = Which says to add, subtract, multiply, or divide two functions, we simply add, subtract, multiply, or divide their individual function rules. Or for a particular value of x, we simply add, subtract, multiply, or divide the related range values. Ex. ( ) 2 3 f x x = - and 2 ( ) 2 g x x = + So (f + g)(x) = f(x) + g(x) = 2 (2 3) ( 2) x x - + + = 2 2 3 2 x x - + + = 2 2 1 x x + - Ex. To find a particular value’s sum, say (f + g)(5) , we can do it in 2 ways: 1) Find the combined function (as we did above), and then substitute the value , 5, for x in the combined function. 2

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Mth141S26n - Sec 2.6 Operations and Composition We can...

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