Lesson 1.5Combination of Functions

Arithmetic Combinations2 Options:

1)Combine the functions (using “x”) with the given operation

2)Plug in a given value into each function, then perform the given operation

You will be asked to find the Domain and Range of the combined functions

ExampleIf f(x) = 2x and g(x) = x + 1, find the following:

(f + g)(x) = f(x) + g(x) =

(f – g)(x) = f(x) – g(x) =

(fg)(x) = f(x) • g(x) =

Composition of FunctionsPlug the inside function into the outside

Notation: (f ο g)(x) = f(g(x))

Again, if given an x value you can work with all numbers.

ExampleIf f(x) = x + 2 and g(x) = 4 – x2, find the following:

(f ο g)(x) =

(g ο f)(x) =

Find both composites when x = 0, 1, 2

Example

Example