Chapter 4: Q. 20 (page 225)

Find the domain of the rational function.
$R (x) = \frac{x}{x^{4} - 1}$

Short Answer

Expert verified

The domain of the given function is $(- \infty, - 1) \cup (- 1, 1) \cup (1, \infty)$

Step by step solution

Step 1. Given information

The given function is $R (x) = \frac{x}{x^{4} - 1}$

Step 2. Find the domain

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

so,

$x^{4} - 1 \neq 0 {(x^{2})}^{2} - 1^{2} \neq 0 (x^{2} - 1) (x^{2} + 1) \neq 0$

We neglect $x^{2} + 1$ because the solution to this will be an imaginary number.

$x^{2} - 1 \neq 0 x^{2} \neq 1 x \neq 1 o r x \neq - 1$

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

Therefore, the domain isrole="math" localid="1646113099270" $(- \infty, - 1) \cup (- 1, 1) \cup (1, \infty)$

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Find the domain of the rational function.
$R (x) = \frac{x}{x^{4} - 1}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the domain

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Find the domain of the rational function.Rx=xx4-1

Short Answer

Step by step solution

Step 1. Given information

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Find the domain of the rational function.
$R (x) = \frac{x}{x^{4} - 1}$