Unformatted text preview: ) f ( x ) By (a) with a function f and scaler α + β = αf ( x ) + βf ( x ) By distributive rule for scalars =( αf )( x ) + ( βf )( x ) By (a) with functions f and scalars α and β =( αf + βf )( x ) By (b) with functions αf and βf Since (( α + β ) f )( x ) = ( αf + βf )( x ) for all x ∈ [ a,b ], they must be the same function. So we have ( α + β ) f = αf + βf . / 1...
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 Spring '08
 samiabdul
 Linear Algebra, Algebra

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