Chapter 8 Section 1 MA1032 Data, Functions & Graphs Sidney - - PowerPoint PPT Presentation

Chapter 8 Section 1

MA1032 Data, Functions & Graphs Sidney Butler

Michigan Technological University

November 28, 2006

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Composition

The function f (g(t)) is said to be a composition of f with g. The function f (g(t)) is defined by using the output of the function g as the input to f . Example Let f (t) =

2 1+t and g(t) = √t.

What happens to Domains and Ranges?

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Decomposition of Functions

Go Backwards! Example Let h(x) = f (g(x)) = ex2+1. Find possible formulas for f (x) and g(x).

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Summary

Composition Domain & Range Decomposition

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Exercise

Let f1(x) = x, f2(x) = 1

x , f3(x) = 1 − x, f4(x) = 1 1−x , f5(x) = x−1 x , and

f6(x) =

x x−1. Note that

f4(f3(x)) = 1 1 − f3(x) = 1 1 − (1 − x) = 1 x = f2(x). That is f4(f3(x)) = f2(x). In fact, if we compose any two of these six functions, we will get one of the six functions. Complete the composition table below.

• f1

f2 f3 f4 f5 f6 f1 f2 f3 f4 f2 f5 f6

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