Function Composition

Here is where we introduce a new operation - composition of functions.  With this definition comes new notation.

This new notation reads “f composed with g.”

The idea is to substitute one function into another function.

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.

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