Composition of Functions Algebraically

Lesson 2: Such a Rad Lesson

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Key Terms

Learning Goals

● square root function
● cube root function
● radical function
● composition of functions

● Use composition of functions to

determine whether two functions are
inverses of each other.

● Solve real-world problems using the

square root and cube root functions

Lesson 2: Such a Rad Lesson

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Essential Question

You have explored the graphs of composite functions. How can you write the
composition of functions algebraically? How can you write the composition of
any function using the notation f(g(x))?

Lesson 2: Such a Rad Lesson

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We say “ g of f of x”
Start with the inside function first and apply to
the outer function.

Lesson 2: Such a Rad Lesson

© Carnegie Learning, Inc

Step1- start with the inside function.

g(-9)= ( -9) +12 = 3

Step 2- the output becomes new input

f(x) = 2(3)²-4(3)-15=
f(x) = 2(9)-12-15=-9

Therefore, f(g(x))= -9

Lesson 2: Such a Rad Lesson

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Step1- start with the inside function.

g(-3)= -4( -3) -3 = _

Step 2- the output becomes new input

f(x) = (_)²-3(_)-4=

Therefore, f(g(x))= _

Lesson 2: Such a Rad Lesson

© Carnegie Learning, Inc

Step1- start with the inside function.

Step 2- the output becomes new input

Therefore, g(f(x))= __

Lesson 2: Such a Rad Lesson

© Carnegie Learning, Inc