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Chapter 4: Q. 35 (page 242)

Solve each inequality algebraically.

(x-1)(x+1)x鈮�0

Short Answer

Expert verified

Solution to the inequality (x-1)(x+1)x鈮�0is (-鈭�,-1]鈭�(0,1].

Step by step solution

01

Step 1. Given information 

We have been given an inequality (x-1)(x+1)x鈮�0.

We have to solve this inequality algebraically.

02

Step 2. Determine the real numbers at which the expression f equals zero and at which the expression f is undefined.  

Assume f(x)=(x-1)(x+1)x.

So, (x-1)(x+1)=0x=-1,1

Also,x=0

03

Step 3. Form the intervals  

Using the values of x found in previous step, we can divide the real numbers in the intervals:

(-鈭�,-1)鈭�(-1,0)鈭�(0,1)鈭�(1,鈭�)

04

Step 4. Select a number in each interval and evaluate f at the number  

Create the following table:

Interval(-鈭�,-1)
(-1,0)
(0,1)
(1,鈭�)
Number chosen
-3
-0.5
0.5
2
Value of ff(-3)=-83f(-0.5)=32
f(0.5)=-32
f(2)=32
Conclusionnegativepositivenegativepositive
05

Step 5. Identify the interval 

Since we want to know where f is negative or zero, we conclude that f(x)鈮�0 in the interval .

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Most popular questions from this chapter

In Problems 25鈥�30, use the graph shown to find

(a) The domain and range of each function

(b) The intercepts, if any

(c) Horizontal asymptote, if one exists

(d) Vertical asymptotes, if any

(e) Oblique asymptote, if one exists

From Ohm鈥檚 law for circuits,

it follows that the total resistance Rtotof two components connected in parallel is given by the equation

Rtot=R1R2R1+R2

where R1,R2are individual resistance.

(a) Let R1=10惟{"x":[[4,4,5,16,24,28,21,4,4,5,33],[44,51,52,52],[66,92],[66,93],[107,107,107,107,108,108,109,111,112,114,114,114,115,115],[129,126,126,126,126,127,129,129,129,138,142,146,149,152,154,159,162,165,173,171,168,163,158,155,147,143,139,138,137,136,136,136,135,135,134,133,132,132,132,130],[196,197,199,203,208,210,215,217,218,219,219,219,220,219,218,216,207,206,206,208,210,213,216,222,229,237,241,243,244,247,248,249,249,249,249,249,249,249,249,248,248,248,255,258,264,267,271,272,273]],"y":[[116,9,9,13,24,38,55,61,61,61,116],[101,90,91,142],[74,74],[93,93],[47.25390625,46.25390625,48.25390625,49.25390625,61.25390625,65.25390625,88.25390625,104.25390625,118.25390625,127.25390625,128.25390625,129.25390625,129.25390625,130.25390625],[58.25390625,64.25390625,66.25390625,70.25390625,73.25390625,80.25390625,87.25390625,88.25390625,89.25390625,103.25390625,106.25390625,109.25390625,109.25390625,109.25390625,108.25390625,103.25390625,99.25390625,97.25390625,68.25390625,64.25390625,61.25390625,58.25390625,56.25390625,55.25390625,55.25390625,55.25390625,54.25390625,54.25390625,53.25390625,53.25390625,54.25390625,55.25390625,56.25390625,58.25390625,59.25390625,62.25390625,64.25390625,65.25390625,65.25390625,72.25390625],[104.25390625,104.25390625,104.25390625,103.25390625,103.25390625,102.25390625,100.25390625,99.25390625,99.25390625,98.25390625,97.25390625,96.25390625,93.25390625,88.25390625,85.25390625,82.25390625,65.25390625,61.25390625,57.25390625,52.25390625,49.25390625,47.25390625,46.25390625,44.25390625,43.25390625,43.25390625,43.25390625,44.25390625,45.25390625,49.25390625,55.25390625,58.25390625,65.25390625,71.25390625,77.25390625,82.25390625,87.25390625,91.25390625,91.25390625,92.25390625,94.25390625,94.25390625,97.25390625,97.25390625,95.25390625,94.25390625,94.25390625,93.25390625,93.25390625]],"t":[[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0],[0,0],[0,0],[1646205525060,1646205525075,1646205525094,1646205525110,1646205525126,1646205525144,1646205525160,1646205525176,1646205525193,1646205525210,1646205525225,1646205525243,1646205525259,1646205525268],[1646205525656,1646205525666,1646205525670,1646205525684,1646205525693,1646205525708,1646205525726,1646205525744,1646205525760,1646205525777,1646205525792,1646205525808,1646205525825,1646205525842,1646205525858,1646205525875,1646205525892,1646205525908,1646205526025,1646205526042,1646205526058,1646205526075,1646205526092,1646205526108,1646205526125,1646205526142,1646205526158,1646205526175,1646205526208,1646205526226,1646205526300,1646205526310,1646205526324,1646205526342,1646205526358,1646205526375,1646205526391,1646205526408,1646205526466,1646205526488],[1646205527135,1646205527170,1646205527191,1646205527207,1646205527224,1646205527240,1646205527257,1646205527273,1646205527290,1646205527307,1646205527323,1646205527340,1646205527357,1646205527373,1646205527390,1646205527406,1646205527490,1646205527507,1646205527524,1646205527540,1646205527557,1646205527574,1646205527590,1646205527606,1646205527623,1646205527640,1646205527656,1646205527673,1646205527690,1646205527707,1646205527724,1646205527740,1646205527757,1646205527773,1646205527790,1646205527806,1646205527823,1646205527840,1646205527856,1646205527873,1646205527889,1646205527906,1646205528050,1646205528055,1646205528074,1646205528090,1646205528106,1646205528123,1646205528156]],"version":"2.0.0"}, and graph Rtotas a function of R2.

(b) Find and interpret any asymptotes of the graph obtained in part (a).

(c) If R2=2R1, what value of R1will yield an Rtotof

17 ohms?

Solve the inequality x2-5x鈮�24. Graph the solution set.

Field Trip Mrs. West has decided to take her fifth grade class to a play. The manager of the theater agreed to discount the regular \( 40 price of the ticket by \) 0.20 for each ticket sold. The cost of the bus, \( 500, will be split equally among each of the students. How many students must attend to keep the cost per student at or below \) 40?

The concentration C of a certain drug in a patient's bloodstream t hours after injection is given by

Ct=50tt2+25

Part (a): Find the horizontal asymptote of Ct. What happens to the concentration of the drug as t increases?

Part (b): Using your graphing utility, graph C=Ct.

Part (c): Determine the time at which the concentration is highest.
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