Function Composition

Here is where we introduce a new operation - composition of functions.  With this definition comes new notation.

YouTube Playlist Introduction to Functions

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.

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(x – 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 g 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:

Multiplying and Dividing Integers

YouTube Playlist on Real Number Operations

Multiplying a negative number by a positive number will result in a negative number. And when multiplying two negative numbers the result will be positive. Be careful when simplifying 5(−6), the operation here is multiplication NOT subtraction so 5(−6) = −30. The rules for division are the same.

(Negative) x (Positive) = (Negative) 

Example: (−7)(+4) = −28

(Negative) x (Negative) = (Positive) 

Example: (−7)(−4) = +28

Also, zero times anything is zero.

Multiply or Divide.

Dividing by zero is undefined. What happens when you try to divide by zero on a calculator?

Zero and Division

Divide.

Video Examples on YouTube: