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Chapter 7: Q. 7.19 (page 649)

Find the domain ofRx=2x2-10x4x2-16x-20.

Short Answer

Expert verified

The domain of Rxis all real numbers, wherex鈮�5andx鈮�-1.

Step by step solution

01

Step 1. Given information

The given expression isRx=2x2-10x4x2-16x-20

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=2x2-10x4x2-16x-20

Set the denominator to zero and solve

4x2-16x-20=04x2-20x+4x-20=0Expandthemiddleterm4x(x-5)+4(x-5)=0writeoutcommonelements(x-5)(4x+4)=0writeoutcommontermx-5=0or4x+4=0Solveforxx=5orx=-1

Hence, the domain is all real numbers except atx=5,-1.

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