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Chapter 3: Q. 42 (page 172)

Explain why the inequality x2-x+1<0has the empty set as solution set.

Short Answer

Expert verified
  • The entire curve lies above the x-axis.
  • The given inequality requires the values for which the function lies below the horizontal axis.
  • So, there is no solution of the inequality.

Step by step solution

01

Step 1. Given Information

The given inequality isx2-x+1<0.

02

Step 2. Find the Intercepts

  • Consider the function f(x)=x2-x+1.
  • The function cannot be factored further.
  • There are no x-intercepts of the curve.
  • The value of f(0)is 1.
  • So, the y-intercept is 1.
  • This implies that the entire curve lies above the x-axis.
  • The given inequality requires the values for which the function lies below the horizontal axis.
  • So, there is no solution of the inequality.

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Most popular questions from this chapter

In Problems 25鈥�32, use the given functions f and g.

(a)f(x)=0(b)g(x)=0(c)f(x)=g(x)(d)f(x)>0

(e)g(x)鈮�0(f)f(x)>g(x)(g)f(x)鈮�1

f(x)=-x2+3g(x)=-3x+3

In Problems 21鈥�28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.

xy=f(x)
-2-4
-1-3.5
0-3
1-2.5
2-2

Find the slope of the line joining the points(2,5) and(-1,3).

Make up a quadratic function that opens down and has only one x-intercept. Compare yours with others in the class. What are the similarities? What are the differences?

What is the domain of the functionx2-16?
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