This new notation reads “

*f*composed with

*g*.”

The idea is to substitute one function into another function.

**Given the functions**.

*f*(*x*) = 5*x*– 4 and*g*(*x*) = 2*x*– 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