Question: Let V be the set of real-valued functions that are defined at each x in the interval (, ). If f = f (x) and

Let V be the set of real-valued functions that are defined at each x in the interval (, ). If f = f (x) and g = g(x) are two functions in V and if k is any scalar, then define the operations of addition and scalar multiplication by ( f + g ) = f ( x ) + g ( x ) k f = k f ( x ) Verify the Vector Space Axioms for the given set of vectors.

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