Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

Precalculus · Chapter 1 · Lesson 1

Practice Worksheet

Composing Functions

The output of one becomes the input of the next.

11 problems · about 22 minutes · TEKS P.2.A, P.2.B

NameDate

Figure — use these to answer the problems

Squaring is one of the two functions being composed here.

y = 1x² + 0x + 0

a1

b0

c0

Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

f(x) = x + 2, g(x) = 5x. f(g(3))?
Answer
f(x) = x + 5, g(x) = 3x. f(g(2))?
Answer
Same functions. g(f(2))?
Answer
f(x) = x², g(x) = x − 1. f(g(4))?
Answer

Build It Up

The same ideas with more to keep track of.

3 problems

f(x) = 2x, g(x) = x/2. f(g(10))?
Answer
Are those two functions inverses? 1 for yes, 0 for no.
Answer
7
Order the steps for evaluating f(g(x)) at a number.
Write 1 to 3 in the boxes to put these in order.
- Substitute the number into g
- Compute the output of g
- Substitute that output into f

Stretch Yourself

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

4 problems

f(x) = x + 4, g(x) = x − 4. f(g(9))?
Answer
Is f(g(x)) generally the same as g(f(x))? 1 for yes, 0 for no.
Answer
Inside First
f(x) = x + 1, g(x) = 2x. What is f(g(3))?
Answer
The Other Order
Same functions. What is g(f(3))?
Answer