The set of all real-valued functions f defined everywhere on the real line and such that f

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The set of all real-valued functions f defined everywhere on the real line and such that f (1) = 0, with the operations defined in Example 4.
In Exercise a set of objects is given, together with operations of addition and scalar multiplication. Determine which sets are vector spaces under the given operations. For those that are not vector spaces, list all axioms that fail to hold.
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