# MA.3 - Compositions of Functions and Inverses of Functions

MA.3  The student will apply compositions of functions and inverses of functions to practical situations and investigate and verify the domain and range of resulting functions.

### UNDERSTANDING THE STANDARD

·  In composition of functions, a function serves as input for another function.

·  The composition of functions f(x) and g(x) can be determined using the graphs of f(x) and g(x).

·  A graph of a function and its inverse are symmetric about the line y = x.

·   (ƒ ◦ ƒ-1)(x) = (ƒ-1 ◦ ƒ)(x) = x

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  MA.31  Determine the composition of functions algebraically and graphically.

·  MA.32  Determine the inverse of a function algebraically and graphically.

·  MA.33  Determine the domain and range of composite functions algebraically and graphically.

·  MA.34  Determine the domain and range of the inverse of a function algebraically and graphically.

### KEY VOCABULARY

Updated: May 29, 2018