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5-44.

A “CHAIN” OF FUNCTIONS Homework Help ✎

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 is written . (Notice that the “inner” function is applied first.)

Let . Draw an arrow diagram and determine the composite function for each part below. Simplifying is not required.

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).