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The Algebra of Functions

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State

Functions combine pointwise by the four operations: (f + g)(x) = f(x) + g(x), likewise the other three.

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For f(x) = x² and g(x) = x + 1 at 2: (f + g)(2) = 4 + 3 = 7, and (fg)(2) = 4 · 3 = 12.

Watch for

The quotient's domain drops g's zeros.

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