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Chapter 4: Q. 5 (page 241)

Use the graph of the function f to solve the inequality.

(a)f(x)>0

(b)f(x)鈮�0

Short Answer

Expert verified

Part a. The solution of the inequality f(x)>0is (0,1)鈭�(2,鈭�).

Part b. The solution of the inequalityf(x)鈮�0is (-鈭�,0]鈭�[1,2].

Step by step solution

01

Part (a) Step 1. Find the values for which the graph is above x axis

To find the solution of f(x)>0, we need to find the values of xfor which the graph is above the xaxis.

From the graph, we can see two intervals role="math" localid="1646169273907" 0<x<1and x>2, for which the graph is above xaxis.

So the solution is given as(0,1)鈭�(2,鈭�).

02

Part (b) Step 1. Find the values for which the graph is below the x axis

To find the solution of f(x)鈮�0, we need to find the values of x for which the graph is below the x axis.

From the graph, we can see two intervals role="math" localid="1646169399580" x鈮�0and 1鈮�x鈮�2, for which the graph is below thex axis.

So the solution is given as (-鈭�,0]鈭�[1,2].

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Most popular questions from this chapter

Solve each inequality algebraically.

x-3x+1>0

Find the real zeros of f. Use the real zeros to factor f.

x3+8x2+11x-20

Graph each rational function using transformations.

R(x)=1+2(x-3)2

Analyze each polynomial function using Steps 1through 8:

f(x)=x4-x3-6x2+4x+8.

In Problems 13鈥�24, find the domain of each rational function.

R(x)=3(x2-x-6)4(x2-9)
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