8.6 Algebra and Composition of Functions. that limit the domain of a function are: The most common rules of algebra Rule 1: You can’t divide by 0. Rule.

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Presentation transcript:

8.6 Algebra and Composition of Functions

that limit the domain of a function are: The most common rules of algebra Rule 1: You can’t divide by 0. Rule 2: You can’t take the square root of a negative number.

Basic function operations Sum Difference Product Quotient

Example 1 Find each function and state its domain: ( f + g )( x ) ( f – g )( x ) ( f ∙ g )( x ) ( f /g )( x )

Find each function and state its domain:

What is the “composition of functions”?

Function Machine x Function Machine g f

Composition of functions Given two functions f and g, the composite function is defined by and is read “ f of g of x.” The domain of is the set of elements x in the domain of g such that g ( x ) is in the domain of f.

Example 3 Evaluate and : You can see that function composition is not commutative!

(Since a radicand can’t be negative in the set of real numbers, x must be greater than or equal to zero.) Example 4 Find the domain of and : (Since a radicand can’t be negative in the set of real numbers, x – 1 must be greater than or equal to zero.)

Summary… Function arithmetic – add the functions (subtract, etc) Addition Subtraction Multiplication Division Function composition Perform function in innermost parentheses first!