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5-44.
  1. A "CHAIN" OF FUNCTIONS
    Remember that composite functions are made by "chaining" simpler functions together. For example, f(x) = 2x2 + 3 is made by chaining the functions h(x) = 2x2 and g(x) = x + 3.

  2. It can be useful to show this idea with an arrow diagram:

  3. arrow diagram

  4. 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.)

  5. 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 ✎

    1. f(x) = g(h(x))

    2. f(x) = h(g(x))

    3. f(x) = g(g(h(x)))

    4. 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).