- Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
*For example, f(x) =2 x³ or f(x) = (x+1)/(x–1) for x ≠ 1.* - Verify by composition that one function is the inverse of another.
- Read values of an inverse function from a graph or a table, given that the function has an inverse.
- Produce an invertible function from a non-invertible function by restricting the domain.

**Subject Area:**Mathematics

**Grade:**912

**Domain-Subdomain:**Functions: Building Functions

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Build new functions from existing functions. (Algebra 1 - Additional Cluster) (Algebra 2 - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

## Related Courses

## Related Access Points

## Related Resources

## Lesson Plan

## Problem-Solving Tasks

## Unit/Lesson Sequence

## Virtual Manipulative

## Student Resources

## Problem-Solving Tasks

This is a simple task touching on two key points of functions. First, there is the idea that not all functions have real numbers as domain and range values. Second, the task addresses the issue of when a function admits an inverse, and the process of "restricting the domain" in order to achieve an invertible function.

Type: Problem-Solving Task

The purpose of this task is to construct and use inverse functions to model a real-life context. Students choose a linear function to model the given data, and then use the inverse function to interpolate a data point.

Type: Problem-Solving Task

Temperature conversions provide a rich source of linear functions which are encountered not only in science but also in our every day lives when we travel abroad. The first part of this task provides an opportunity to construct a linear function given two input-output pairs. The second part investigates the inverse of a linear function while the third part requires reasoning about quantities and/or solving a linear equation.

Type: Problem-Solving Task

In this task, students explore the inverse relationship between an exponential function and a logarithmic function. The task is to determine the relevant composite functions, their graphs, and the domain and range of each.

Type: Problem-Solving Task

Unit conversion problems provide a rich source of examples both for composition of functions (when several successive conversions are required) and inverses (units can always be converted in either of two directions).

Type: Problem-Solving Task

In this task, students are asked to analyze a function and its inverse when the function is given as a table of values. In addition to finding values of the inverse function from the table, they also have to explain why the given function is invertible.

Type: Problem-Solving Task

This task illustrates several components of standard MAFS.912.F-BF.2.4.c: Find Inverse Functions. Here, instead of presenting two functions and asking the students to decide which on is invertible, students are asked to complete a table of input-output pairs for the functions in such a way that one of the functions is invertible and the other one is not.

Type: Problem-Solving Task

## Virtual Manipulative

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.

Type: Virtual Manipulative

## Parent Resources

## Problem-Solving Tasks

This is a simple task touching on two key points of functions. First, there is the idea that not all functions have real numbers as domain and range values. Second, the task addresses the issue of when a function admits an inverse, and the process of "restricting the domain" in order to achieve an invertible function.

Type: Problem-Solving Task

The purpose of this task is to construct and use inverse functions to model a real-life context. Students choose a linear function to model the given data, and then use the inverse function to interpolate a data point.

Type: Problem-Solving Task

Temperature conversions provide a rich source of linear functions which are encountered not only in science but also in our every day lives when we travel abroad. The first part of this task provides an opportunity to construct a linear function given two input-output pairs. The second part investigates the inverse of a linear function while the third part requires reasoning about quantities and/or solving a linear equation.

Type: Problem-Solving Task

In this task, students explore the inverse relationship between an exponential function and a logarithmic function. The task is to determine the relevant composite functions, their graphs, and the domain and range of each.

Type: Problem-Solving Task

Unit conversion problems provide a rich source of examples both for composition of functions (when several successive conversions are required) and inverses (units can always be converted in either of two directions).

Type: Problem-Solving Task

In this task, students are asked to analyze a function and its inverse when the function is given as a table of values. In addition to finding values of the inverse function from the table, they also have to explain why the given function is invertible.

Type: Problem-Solving Task

This task illustrates several components of standard MAFS.912.F-BF.2.4.c: Find Inverse Functions. Here, instead of presenting two functions and asking the students to decide which on is invertible, students are asked to complete a table of input-output pairs for the functions in such a way that one of the functions is invertible and the other one is not.

Type: Problem-Solving Task

## Virtual Manipulative

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.

Type: Virtual Manipulative