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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

In Exercises 73–78, determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

74. If gf is defined at x = a, then fg must also be defined at x = a.

To determine
Whether the statement “If gf is defined at x=a , then fg must also be defined at x=a ”, is true or false.

Explanation

Counter example

Consider first function f(x)=12x2 .

Consider second function g(x)=x2a2 .

The composite function gf is,

gf=g[f(x)]=(12x2)2a2=14x4a2

From above equation, it is seen that the composite function gf is defined at x=a

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