**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