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Definition. Let f and g be functions.

1. Their sum, denoted by f + g is the function denoted by (f + g)(x) = f(x) + g(x)

2. Their difference, denoted by f - g is the function denoted by (f - g)(x) = f(x) - g(x)

3. Their product, denoted by fg is the function denoted by (fg)(x) = f(x) * g(x)

4. Their quotient, denoted by f/g, is the function denoted by (f / g)(x) = (f(x)) / g * (x) excluding the values of x where g(x) = 0 .

5. The composite function denoted by (f deg * g)(x) = f(g(x)) . The process of obtaining a composite function is called function composition.​