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Chapter 3: Q. 4 (page 171)

In problems 3-6, use the figure to solve each inequality.

a)g(x)<0

b)g(x)鈮�0

Short Answer

Expert verified

a)(-鈭�,-1)or(4,鈭�)

b)[-1,4]

Step by step solution

01

Part (a) Step 1. Given Information 

It is given that, g(x)<0and the graph is,

02

Part (a) Step 2. Observe the graph 

  • From the graph, it is observed that the value of y=g(x)is negative for localid="1646305079342" x<-1or x>4.
  • In set builder form, for g(x)<0, localid="1646305088829" {x|x<-1orx>4}. Also, in interval notation it is denoted as localid="1646305102141" (-鈭�,-1)or (4,鈭�).
03

Part (b) Step 1. Given Information  

It is given that, g(x)鈮�0and the graph is,

04

Part (b) Step 2. Observe the graph  

  • From the graph, it is observed that the value of y=g(x)is positive or equal to 0 for -1鈮�x鈮�4.
  • In set builder form, for g(x)鈮�0, {x|-1鈮�x鈮�4}. Also, in interval notation it is denoted as [-1,4].

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