Concept

Function Operations

f (x)

and

g (x),

there are four function operations that can be applied to them — addition, subtraction, multiplication, and division. However, to perform any of these operations, the domains of the functions must intersect each other. Next, the formulas for combining functions are written.

(f + g) (x) (f - g) (x) (f \cdot g) (x) (\frac{f}{g}) (x) = f (x) + g (x) = f (x) - g (x) = f (x) \cdot g (x) = \frac{f ( x )}{g ( x )}, g (x) \neq = 0

For the last case, the denominator has to be different from zero. As with algebraic operations, only the sum and product of functions are commutative. In the next table, the function operations are illustrated.

Applet calculating sum, difference, product, and division of f(x)=x-4 and g(x)=x-2

Once two functions are combined, the domain of the resulting function is the intersection of both domains, excluding the values that make the denominator equal to zero.

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