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Chapter 4: Q. 14 (page 225)

Find the domain of the rational function.
$R (x) = \frac{5 x^{2}}{3 + x}$

Short Answer

Expert verified

The domain of the given function is $(- \infty, - 3) \cup (- 3, \infty)$

Step by step solution

01

Step 1. Given information

The given function is $R (x) = \frac{5 x^{2}}{3 + x}$

02

Step 2. Find the domain

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

So,

$3 + x \neq 0 x \neq - 3$

Thus, the domain of the given function is all real numbers except $- 3$ .

Therefore the domain is $(- \infty, - 3) \cup (- 3, \infty)$

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Most popular questions from this chapter

Find the domain of the rational function.

$R (x) = \frac{x}{x^{4} - 1}$

In Problems 21–32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

$f (x) = 2 x^{5} - x^{4} - x^{2} + 1$

Find the real zeros of f. Use the real zeros to factor f.

$f (x) = 4 x^{4} - 15 x^{3} - 8 x^{2} + 15 x + 4$

Solve the inequality algebraically.

$x^{4} < 9 x^{2}$

Use the Factor Theorem to prove that $x - c$ is a factor of

$x^{n} - c^{n}$ for any positive integer n.

See all solutions

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