Operations With Functions
||(f + g)(x) = f(x) + g(x)
||(f - g)(x) = f(x) - g(x)
||(f Â· g)(x) = f(x)
The domain of the sum, difference and product of f and g consist of all real numbers for which
f and g
are defined. The domain of the quotient of f and g consists of all real numbers for which
f and g are defined and g ≠ 0.
Composition of Functions
Definition: The composite function, f of g, is denoted by f g and defined by (f
o g)(x) = f(g(x)).
The domain of f o g is the subset of the domain of g for which f g is defined.
The composite function g o f is defined by (g o f)(x) = g(f(x).
The domain of g o f is the subset of the domain of f for which g o f is defined.