100921 Notes Inverses of functions

100921 Notes Inverses of functions - Name Date Honors...

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Name Honors Algebra 2 (J. Sera) Date _________________________ Class notes Inverses of functions Pairs of inverse functions Here are some ways to tell whether two functions f ( x ) and g ( x ) are inverses of each other. Using composites: f ( x ) and g ( x ) are inverses if f ( g ( x )) = x and g ( f ( x )) = x . Thinking about function rules: f ( x ) and g ( x ) are inverses if their rules “reverse” or “undo” each other. Using their tables: f ( x ) and g ( x ) are inverses if their tables are related by exchanging the input and output columns. Using their graphs: f ( x ) and g ( x ) are inverses if whenever ( a , b ) is on the graph of one function, ( b , a ) is on the graph of the other function. Using a reflection property of graphs: f ( x ) and g ( x ) are inverses if their graphs are “mirror images” of each other across the diagonal line y = x . Making the inverse of a function If you start with just one function f ( x ), here are some ways to make its inverse. Making a table: Take the table of f ( x ), and exchange the input and output columns.
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