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Chapter 11: Q. 557RE (page 1069)

In the following exercises, find the domain of the function and write the domain in interval notation.

F(x)=x+3x-2

Short Answer

Expert verified

Domain isx鈭�(-鈭�,-3]鈭�(2,鈭�)

Step by step solution

01

Given information 

Domain ofF(x)=x+3x-2

02

Solution

We have

F(x)=x+3x-2

Here

x+3x-2鈮�0

Taking the intervals
(-鈭�,-3],(-3,2],(2,鈭�)

Checking

In localid="1663766527461" (-鈭�,-3]value of x+3x-2鈮�0

In localid="1663766706310" (-3,2]value of localid="1663766578080" x+3x-2<0is not defined or negative

In localid="1663766538327" (2,鈭�)value of x+3x-2鈮�0

Hence the domain is

x鈭�(-鈭�,-3]鈭�(2,鈭�)

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