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Chapter 4: Q. 24 (page 225)

In Problems 13鈥�24, find the domain of each rational function.

R(x)=-2(x2-4)3(x2+4x+4)

Short Answer

Expert verified

The domain of the rational function R(x)=-2(x2-4)3(x2+4x+4)is {xx鈭�鈩�,x鈮�-2}

Step by step solution

01

Step 1. Given

The rational functionR(x)=-2(x2-4)3(x2+4x+4)

To find the domain of the given rational function.

02

Step 2. Factor the denominator.

Factorize the denominator.

x2+4x+4=x2+2x+2x+4=(x+2)(x+2)=(x+2)2

03

Step 3. Use the zero-Product property

By using Zero-Product property,

x+2=0

04

Step 4. Solve the equation

Solve the equations

x+2=0x=-2

The domain of the function is {xx鈭�鈩�,x鈮�-2}

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