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Cogito

Integrated Math 3 · Chapter 8 · Lesson 2

Practice Worksheet

Combining and Composing Functions

Building complicated models from simple parts.

12 problems · about 21 minutes · F-BF.A.1

NameDate

Figure — use these to answer the problems

Composing with a square root imposes its domain restriction on whatever goes inside.
-8-8-6-6-4-4-2-222446688
y = 1√x + 0
  • Point(4, 2)
a, coefficient1
Point on the curve4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. f(x) = 3x and g(x) = x + 2. What is f(g(4))?

    Answer

  2. What must hold for a composition to make sense in context?

    • The inner output units must match the outer input units.
    • Both functions must be the same type.

  3. f(x) = 2x and g(x) = x + 3. What is f(g(4))?

    Answer

  4. f(x) = x² and g(x) = x + 1. What is f(g(3))?

    Answer

  5. f(x) = 3 and g(x) = 5. What is (f + g)(x)?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. f(x) = √x and g(x) = x − 9. Smallest x in the domain of f(g(x))?

    Answer

  2. A quotient f ÷ g. Which x values are excluded? 1 where g is zero, 2 where f is zero.

    Answer

  3. u(h) = 12h. How many units in 5 hours?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put the steps for a composite domain in order.

    Write 1 to 4 in the boxes to put these in order.

    • Find the domain of the inner function.
    • Require the inner output to lie in the outer domain.
    • Combine both restrictions.
    • Only then simplify the expression.

  2. f(x) = x + 5 and g(x) = 2x. What is f(g(3))?

    Answer

  3. The Composition

    u(h) = 12h and c(u) = 5u. What is c(u(2))?

    Answer

  4. The Order

    f(x) = 2x and g(x) = x + 3. What is g(f(4))?

    Answer