A transformation \( T: V \to \mathbb{R} \) is a linear functional if it satisfies two properties for all functions \( f, g \in V \) and scalars \( c \in \mathbb{R} \):
- Additivity: \( T(f + g) = T(f) + T(g) \)
- Homogeneity: \( T(cf) = cT(f) \)
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