Chapter 4: Q. 23 (page 225)

In Problems 13–24, find the domain of each rational function.
$R (x) = \frac{3 (x^{2} - x - 6)}{4 (x^{2} - 9)}$

Short Answer

Expert verified

The domain of the rational function $R (x) = \frac{3 (x^{2} - x - 6)}{4 (x^{2} - 9)}$ is ${x x \neq - 3, x \neq 3}$

Step by step solution

Step 1. Given

The rational function $R (x) = \frac{3 (x^{2} - x - 6)}{4 (x^{2} - 9)}$

To find the domain of the given rational function.

Step 2. Factor the denominator.

Factorize the denominator.

$4 (x^{2} - 9) = 4 (x^{2} - 3^{2}) = 4 (x + 3) (x - 3)$

Step 3. Use the zero-Product property

By using Zero-Product property,

$(x + 3) (x - 3) = 0$

Either $x + 3 = 0$ or

$x - 3 = 0$

Step 4. Solve the equation

Solve the equations

$x + 3 = 0 x = - 3$

And $x - 3 = 0 x = 3$

The domain of the function is ${x x \neq - 3, x \neq 3}$

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In Problems 13–24, find the domain of each rational function.
$R (x) = \frac{3 (x^{2} - x - 6)}{4 (x^{2} - 9)}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Factor the denominator.

Step 3. Use the zero-Product property

Step 4. Solve the equation

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In Problems 13–24, find the domain of each rational function.R(x)=3(x2-x-6)4(x2-9)

Short Answer

Step by step solution

Step 1. Given

Step 2. Factor the denominator.

Step 3. Use the zero-Product property

Step 4. Solve the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Logic and Functions

Geometry

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In Problems 13–24, find the domain of each rational function.
$R (x) = \frac{3 (x^{2} - x - 6)}{4 (x^{2} - 9)}$