Learn Before
Example: Finding the Inverse of the Function
To find the inverse of the one-to-one function represented by the set of ordered pairs , reverse the -values and -values in each of its ordered pairs. This yields the inverse function: .
Additionally, the domain and range of the inverse function correspond to the reversed coordinates of the original function. The domain of the inverse function is the set of all its first coordinates: . The range of the inverse function is the set of all its second coordinates: .
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.10 Exponential and Logarithmic Functions - Intermediate Algebra @ OpenStax
Algebra
Related
Domain and Range of an Inverse Function
Example: Finding the Inverse of the Function
Inverse Function Notation
Example: Finding the Inverse of the Function
Finding an Inverse Function Using an Algebraic Equation
A company directory uses a function to map employee badge numbers to their assigned office room numbers: . To create a reverse lookup that finds a badge number based on a room number, the system uses the inverse function . Which of the following represents the set of ordered pairs for ?
An HR database uses a one-to-one function to map an employee's starting year () to their earned vacation days (), written as the ordered pair . To define the inverse function that maps vacation days back to the starting year, you must form new ordered pairs by ________ the - and -coordinates of each original pair.
Retail Inventory Reverse Lookup
In a company's asset management database, a one-to-one function is used to link unique hardware tags to specific office workstations. Match each original assignment pair (Hardware Tag, Workstation ID) with its corresponding inverse pair (Workstation ID, Hardware Tag) used for reverse-lookup audits.
A corporate security system uses a function to map unique employee identification numbers () to their designated office security codes () using the set of ordered pairs . To define the inverse function , which identifies an employee identification number when given a security code, you must reverse each ordered pair to .
Learn After
A quality control technician uses a function to record the relationship between a machine's setting and the resulting output length in millimeters: . To determine which machine setting corresponds to a desired output length, the technician needs the inverse function . Which of the following sets represents the inverse function ?
A telecommunications company uses a function to link the number of additional data lines a business has (input) to their monthly service fee in dollars (output). To find the number of lines based on a specific bill amount, the billing department uses the inverse function . Match each monthly bill amount (the input for ) with the corresponding number of data lines (the output for ).
An environmental agency uses a function where the input is the number of hours a filtration system runs and the output is the number of pollutants removed in grams. To determine the hours needed for a specific amount of pollutant removal, the agency uses the inverse function .
True or False: The domain of the inverse function is .
Inverse Function for Logistics Mapping
A manufacturing plant maps the number of hours a machine runs to the number of maintenance checks required using the function . To work backwards from the number of maintenance checks to find the hours run, the plant supervisor uses the inverse function . In the inverse function , if the input is 10, the corresponding output is ____.