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Chapter 7: Q. 372 (page 732)

Solve each rational function inequality and write the solution in interval notation.

Given the functionR(x)=(x+1)(x+3), find the values of x that make the function less than or equal to 0.

Short Answer

Expert verified

Solution for inequality isx鈭�(-3,-1].

Step by step solution

01

Step 1. Given Information

Given that the function isR(x)=(x+1)(x+3)鈮�0.

02

Step 2. Critical point

To find the critical point,

(x+1)=0x=-1(x+3)=0x=-3Atx=-1,R(x)=02=0Atx=-3,R(x)=-2-0=鈭�

The polynomial function which is undefined will not included in interval.

03

Step 3. Number line

It can be drawn as,

04

Step 4. Testing of polynomial expression

On testing the polynomial expression sign in every interval, it can be indicated.

(x+1)(x+3)鈮�0,(-3,-1]Thus,R(x)鈮�0forx鈭�(-3,-1].

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