### Home > CALC > Chapter 5 > Lesson 5.1.4 > Problem 5-44

A "CHAIN" OF FUNCTIONS

Remember that composite functions are made by "chaining" simpler functions together. For example,*f*(*x*) = 2*x*^{2}+ 3 is made by chaining the functions*h*(*x*) = 2*x*^{2}and*g*(*x*) =*x*+ 3.It can be useful to show this idea with an arrow diagram:

Above is an arrow diagram for

*h*followed by*g*, which would be written*f*(*x*) =*g*(*h*(*x*)). (Notice that the "inner" function is applied first.)Let

*h*(*x*) = tan*x*+ 5 and*g*(*x*) = (*x*+ 3)^{2}. Draw an arrow diagram and determine the composite function for each*f*(*x*) below. Simplifying is not required. Homework Help ✎*f*(*x*) =*g*(*h*(*x*))*f*(*x*) =*h*(*g*(*x*))*f*(*x*) =*g*(*g*(*h*(*x*)))*f*(*x*) =*h*(*g*(*g*(*x*)))

Refer to example above and hint in part (a).

Refer to example above and hint in part (a).

Refer to example above and hint in part (a).