Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Find g × f when f(x)=1/3x-3 and g(x)=3x+1
Expert Solution
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Step 1: Introduction to the Question

Given: The functions f open parentheses x close parentheses and g open parentheses x close parentheses,  defined as, 

f left parenthesis x right parenthesis equals fraction numerator 1 over denominator 3 x minus 3 end fraction comma g left parenthesis x right parenthesis equals 3 x plus 1.

Aim: To determine the product of two functions, i.e., g cross times f.

Definition: The Product of Two Functions:

Given two functions defined as, f left parenthesis x right parenthesis and g left parenthesis x right parenthesis then the product of these two functions is defined by, left parenthesis f space cross times space g right parenthesis left parenthesis x right parenthesis space equals space f left parenthesis x right parenthesis space cross times space g left parenthesis x right parenthesis, where x is in the domain of both f and g.

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