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Chapter 4: Q. 82 (page 243)

Make up an inequality that has no solution. Make up one that has exactly one solution.

Short Answer

Expert verified

The inequality that has no solution is $\sin (x) > 1$ and the inequality that has exactly one solution is $x^{2} \leq 0$ .

Step by step solution

01

Given information

The inequality which has no solution and another inequality which has exactly one solution.

02

Determine the inequality

Since, the value of sine function does not exceed 1 , the inequality with no solutions can be:

$\sin (x) > 1$

Since square of an expression cannot be less than 0 ,

$x^{2} \geq 0$

To get only one solution, the inequality can be modified as:

$x^{2} \leq 0$

03

Write the conclusion

The inequality which has no solution is $\sin (x) > 1$ .

The inequality which has exactly one solution is $x^{2} \leq 0$

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Most popular questions from this chapter

Solve the given inequality algebraically.

$x^{3} > 1$

Use the Factor Theorem to prove that $x - c$ is a factor of

$x^{n} - c^{n}$ for any positive integer n.

In Problems 57– 62, find the real zeros of f. If necessary, round to two decimal places.

$f (x) = x^{4} + 1.2 x^{3} - 7.46 x^{2} - 4.692 x + 15.2881$

In Problems 57– 62, find the real zeros of f. If necessary, round to two decimal places.

$f (x) = x^{3} + 42.2 x^{2} - 664.8 x + 1490.4$

Analyze each polynomial function using Steps $1$ through $8$ :

$f (x) = x^{4} + x^{3} - 3 x^{2} - x + 2$ .

See all solutions

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