Showing posts with label composition. Show all posts
Showing posts with label composition. Show all posts

Function Composition

Here is where we introduce a new operation - composition of functions.  With this definition comes new notation.
This new notation reads “f composed with g.”
The idea is to substitute one function into another function.

Given the functions f(x) = 5x – 4 and g(x) = 2x – 1.
Composition of functions is not necessarily a commutative operation, in other words, order matters.

Instructional Video: Composite Functions

Given the functions f(x) = x^2 – 9 and g(x) = x – 3.
Given the functions f(x) = x^2 + 1 and g(x) = sqrt(– 1) where ( x >= 1 ).
At this point we must understand what happens to the domain of a composite function. In the above example it might appear that f o g has a domain of all real numbers.  In fact, the domain is restricted to [1, inf) because that is the domain of g.  The domain of f o consists of all the values in the domain of g that are also in the domain of f.

Given f and g find f o g and state its domain.

YouTube Videos:








Logarithms, Exponentials, and Equations

Notes and video examples covering the following topics:

Function Composition:
    
Inverse Functions:
 
 
 
 
Exponential Functions and Their Graphs
   
The Natural Exponential Function
   
Logarithmic Functions
     
Graphing Logarithmic Functions

Change of Base Formula
Properties of the Logarithm
        
Solving Exponential Equations
         
Solving Logarithmic Equations
         
Compound Interest Problems

Exponential Growth and Decay