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Algebra 2 · Chapter 6 · Lesson 6.5 · Printable PDF

Domain of a Composition Worksheet with Answer Key

5 problems on the domain of a composition: finding the domain in interval notation for pairs of functions, square roots and fractions, endpoints included or not, comparing f of g with g of f, a table, and a kayak rental word problem. 2 pages, with a worked answer key.

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Printable Domain of a composition worksheet with answer key - Algebra 2 (Page 1 PDF preview)
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What's on the worksheet

  1. Find the domain of f composed with g for each pair, in interval notation.
    f(x) = \sqrt{x}, \; g(x) = 5 - 2xf(x) = \dfrac{1}{x^2 - 9}, \; g(x) = x + 1f(x) = \sqrt{x - 3}, \; g(x) = \sqrt{x}f(x) = \sqrt{x - 2}, \; g(x) = \lvert x + 1 \rvertf(x) = \dfrac{1}{x - 2}, \; g(x) = x^2 + 2
  2. Find the domain of a composition with a square root in the denominator and explain the endpoints.
  3. Simplify f of g and g of f, find both domains and compare them.
  4. Use the table for g and the formula for f to find the domain of the composition.
  5. Word problem: kayaks needed for a group at a rental shop with 9 kayaks.

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Domain of a composition: the lesson ›

More Chapter 6 worksheets: Combined, composite and inverse functions