lesson 1 5 combination of functions n.
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Lesson 1.5 Combination of Functions - PowerPoint PPT Presentation


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Lesson 1.5 Combination of Functions. Arithmetic Combinations. 2 Options: Combine the functions (using “x”) with the given operation 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. Example

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slide2

Arithmetic Combinations

2 Options:

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

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

slide3

Example

If 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) =

slide4

Composition of Functions

Plug 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.

slide5

Example

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

(f οg)(x) =

(g οf)(x) =

Find both composites when x = 0, 1, 2