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Chapter 7: Q. 7.20 (page 639)

Find the domain ofRx=4x2-16x8x2-16x-64.

Short Answer

Expert verified

The domain ofR(x)is all real numbers, wherex鈮�4andlocalid="1644905259326" x鈮�-2.

Step by step solution

01

Step 1. Given information

The given expression isRx=4x2-16x8x2-16x-64

02

Step 2. Concept used

The domain of the rational function is all real numbers except the values that make the denominator equal to zero.

Procedure to find the domain:

  • Set the denominator equal to zero.
  • Solve the equation.
  • The domain is all real numbers except the values found in the previous step.
03

Step 3. Find the domain

Rx=4x2-16x8x2-16x-64

Set the denominator to zero and solve

8x2-16x-64=0x2-2x-8=0Writeoutfactor8x2-4x+2x-8=0Expandthemiddletermx(x-4)+2(x-4)=0Writeoutcommonelements(x-4)(x+2)=0Writeoutcommontermx-4=0orx+2=0Solveforxx=4orx=-2

Hence, the domain is all real numbers except atx=4,-2.

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