The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

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WORKSHEET 8.9: FINDING THE COMPOSITE

OF TWO FUNCTIONS

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To find the composite of two functions, follow the steps below:

1. Find the two functions that will be combined.


2. Check the notation. The range of the function enclosed in parentheses will be substi-
   tuted forxin the other function.


3. Simplify the output.

EXAMPLE

Iff(x)= 3 x+ 1 andh(x)= 4 x− 2 , findf(h(x)).

Thefandhfunctions will be combined. The range ofh(x),whichis 4 x− 2 , will be substituted

forxinf(x).f(h(x))= 3 ( 4 x− 2 )+ 1 = 12 x− 5

DIRECTIONS: Find the composites below by using these functions:

f(x)= 3 x+ 1 , g(x)=x^2 , h(x)= 4 x− 2 ,andI(x)=− 2 x.

1. f(g(x)) 2. g(h(x)) 3. f(h(x)) 4. h(f(x))


2. g(I(x)) 6. f(I(x)) 7. g(f(x)) 8. h(I(x))


3. I(g(x)) 10. I(f(x)) 11. h(g(x)) 12. I(h(x))

CHALLENGE:Bridget found two functions:j(x)=x+1andk(x)=x−1. She

said thatj(k(x))=k(j(x)). Do you agree? Explain your reasoning.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.