Given the functions f(x) = 5x – 4 and g(x) = 2x – 1.
Composition of functions is not necessarily a commutative operation, in other words, order matters.
Instructional Video: Composite Functions
Given the functions f(x) = x^2 – 9 and g(x) = x – 3.
Given the functions f(x) = x^2 + 1 and g(x) = sqrt(x – 1) where ( x >= 1 ).
At this point we must understand what happens to the domain of a composite function. In the above example it might appear that f o g has a domain of all real numbers. In fact, the domain is restricted to [1, inf) because that is the domain of g. The domain of f o g consists of all the values in the domain of g that are also in the domain of f.
Given f and g find f o g and state its domain.