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Chapter 4: Q. 12 (page 241)

Solve the inequality by using the graph of the function.
Solve $f (x) > 0$ , where
$f (x) = (x - 1) (x + 3)^{2}$

Short Answer

Expert verified

The solution of the inequality is $(1, \infty)$ .

Step by step solution

01

Step 1. Given Information

We are given a function,

$f (x) = (x - 1) (x + 3)^{2}$

02

Step 2. Graphing the function

The graph of the function is as follows,

03

Step 3. Solve the inequality

As seen from the graph, $f (x) > 0$ for the interval $(1, \infty)$ .

Hence the solution is $(1, \infty)$ .

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Most popular questions from this chapter

In Problems 21–32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

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

Write a few paragraphs that provide a general strategy for graphing a polynomial function. Be sure to mention the following: degree, intercepts, end behavior, and turning points.

Find the domain of the rational function.

$H (x) = \frac{3 x^{2} + x}{x^{2} + 4}$

True or False : The graph of $f (x) = \frac{x}{x - 3}$ is above the x-axis for $x < 0$ or $x > 3$ , so the solution set of the inequality $\frac{x}{x - 3} \geq 0$ is ${x : x \leq 0 o r x \geq 3}$ ..

In Problems 39–56, find the real zeros of f. Use the real zeros to factor f.

$f (x) = 4 x^{5} + 12 x^{4} - x - 3$

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