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Chapter 4: Q. 20 (page 225)

Find the domain of the rational function.

Rx=xx4-1

Short Answer

Expert verified

The domain of the given function is鈥�-鈭�鈥�,鈥�-1鈭�-1,鈥�1鈭�1,鈥�鈭�鈥�

Step by step solution

01

Step 1. Given information

The given function isR(x)=xx4-1

02

Step 2. Find the domain 

For the domain, the denominator should not be equal to zero.

so,

x4-1鈮�0x22-12鈮�0x2-1x2+1鈮�0

We neglect x2+1because the solution to this will be an imaginary number.

x2-1鈮�0x2鈮�1x鈮�1orx鈮�-1

Thus, the domain of the given function is all real numbers except -1and 1.

Therefore, the domain isrole="math" localid="1646113099270" 鈥�-鈭�鈥�,鈥�-1鈭�-1,鈥�1鈭�1,鈥�鈭�鈥�鈥�

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Most popular questions from this chapter

In Problems 63鈥�72, find the real solutions of each equation.

2x3+3x2+2x+3=0

Find the domain of the rational function.

G(x)=x-3x2+1

Solve the inequality algebraically.

x4<9x2

Write a few paragraphs that provide a general strategy for graphing a polynomial function. Be sure to mention the following: degree, intercepts, end behavior, and turning points.

True or False. If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients give rise to the horizontal asymptote.
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