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Chapter 3: Q. 6 (page 171)

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

a) f(x)<g(x)

b)f(x)≥g(x)

Short Answer

Expert verified

(a) [-2,1]

(b)(-∞,-3]or[1,∞)

Step by step solution

01

Part (a) Step 1. Given Information   

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

02

Part (a) Step 2. Observe the graph   

  • From the graph, it is observed that the value of f(x)is less than g(x)for -3<x<1.
  • In set builder form, for f(x)<g(x), {x|-3<x<1}. Also, in interval notation it is denoted as(-3,1).
03

Part (b) Step 1. Given Information    

It is given that f(x)≥g(x)and the graph is,

04

Part (b) Step 2. Observe the graph    

  • From the graph, it is observed that the value of f(x)is greater than or equal to g(x)for role="math" localid="1646315317778" x≤-3orx≥1.
  • In the set builder form, for f(x)≥g(x), role="math" localid="1646315330982" {x|x≤-3orx≥1}. Also, in interval notation it is denoted asrole="math" localid="1646315359419" (-∞,-3]or[1,∞).

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