Answered: Find g × f when f(x)=1/3x-3 and…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Find g × f when f(x)=1/3x-3 and g(x)=3x+1

Expert Solution

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 $g$ .