Questions on Composition of Functions


What's On This Page

This page contains sample problems on function composition. They are for Self-assessment and Review.

Each problem (or group of problems) has an "answer button" ANSWER which you can click to look at an answer. Some solutions have a "further explanation button" Explain which you can click to see a more complete, detailed solution.

What to Do

To gain the most benefit from these problems,

Work the problems on your own. Write down your solutions BEFORE looking at any answers.

If you have difficulties with this material, please contact your instructor. (See Getting Help in Stage 1.) Function composition basic to calculus. If you have trouble with these exercises, you will have difficulty with many examples and applications in CalculusQuestTM. We recommend either catching up VERY FAST or considering solidifying your background with a different course.


  1. Let f(x) = 1/x and g(x) = x2 + 2. Find the following functions:

    1. f(g(x))

    2. g(f(x))

    ANSWER

  2. Repeat the instructions in the previous question for the functions:
    f(x) = sqrt(x+1), g(x) = x2
    ANSWER

  3. Express the following functions as a composition of simpler functions.

    Example: sin(x2) is the composition f g of f(x) = sin(x) and g(x) = x2.

    1. ln(x + 3)

    2. tan2(x)

    3. sqrt(sin3(x))

    ANSWER

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