Review of 1.4 (Graphing)Compare the graph with

Compare the graph with

Compare the graph with

y x 1y x

| |y x | 2 | 3y x

3y x 3( 3) 4y x

1.5 Combinations of Functions

Arithmetic CombinationsThe sum, difference, product and

quotient of two functions f and g are defined as follows.

1)Sum (f + g)(x) = f(x) + g(x)

2)Difference (f - g)(x) = f(x) - g(x)

3)Product (f * g)(x) = f(x) * g(x)

4)Quotient (f / g)(x) = f(x) / g(x)

Example 1. Let f(x) = x2 + 3x -7, and g(x) = 4x +5.

Find (f + g)(x) ,(f - g)(x) ,(f * g)(x) ,(f / g)(x)

Now find (f + g)(3)

Example 2. Let f(x) = x2 - 9, and g(x) = x - 3. Simplify the formula for f / g(x).

Composition of FunctionsThe composition of two functions f and g is

defined by (f ° g)(x) = f(g(x)).

Example: Find andgiven that

( )f g x ( )g f x( ) 3, ( ) 3 4f x x g x x

ExampleLet f(x) = x2 - x + 1, and g(x) = 3x - 2.

( ) ( )Find f g x and g f x (5) (5)Find f g and g f