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**Standard(s): **
[MA2015] AL2 (9-12) 35 :

[MA2015] PRE (9-12) 21 :

[MA2015] PRE (9-12) 22 :

[MA2015] PRE (9-12) 23 :

[MA2015] PRE (9-12) 24 :

[MA2015] ALT (9-12) 35 :

35 ) Find inverse functions. [F-BF4]

a. 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. [F-BF4a]

Example: *f*(*x*) =2*x*^{3} or *f*(*x*) = (*x*+1)/(*x*-1) for *x* ≠ 1.

[MA2015] PRE (9-12) 21 :

21 ) (+) Verify by composition that one function is the inverse of another. [F-BF4b]

[MA2015] PRE (9-12) 22 :

22 ) (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. [F-BF4c]

[MA2015] PRE (9-12) 23 :

23 ) (+) Produce an invertible function from a non-invertible function by restricting the domain. [F-BF4d]

[MA2015] PRE (9-12) 24 :

24 ) (+) Understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents. [F-BF5]

[MA2015] ALT (9-12) 35 :

35 ) Find inverse functions. [F-BF4]

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. [F-BF4a]

Example *f*(*x*) = 2*x*^{3} or *f*(*x*) = (*x*+1)/(*x*-1) for *x* ≠ 1.

In Module 3, Topic C students study inverse functions, being careful to understand when inverse functions do and do not exist, working to restrict the domain of a function to produce an invertible function. They compare and create different representations of functions including tables and graphs. Students compose functions to verify that one function is the inverse of another and work with tables of data to identify features of inverse functions. Special emphasis is given to the inverse relationship between exponential and logarithmic functions.

**Note: This module is identified as Precalculus and Advanced Topics in the EngageNY curriculum. It also corresponds to the Algebra II and Algebra II with Trigonometry Alabama Courses of Study.**