Question

Determine the domain of each function. $$ h(x)=\frac{x^{3}-64 x}{x^{2}+81} $$

Name: Problem 24, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2020-06-26T01:45:00-08:00
Duration: 11 s
Channel: Michelle Nguyen
Description: Determine the domain of each function. h(x)=(x^3-64 x)/(x^2+81)

   Determine the domain of each function.
$$
h(x)=\frac{x^{3}-64 x}{x^{2}+81}
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 6, Problem 24

Instant Answer

Solved by Expert Michelle Nguyen

06/26/2020

Step 1

In this case, the only restriction would be if the denominator is equal to 0, as division by 0 is undefined. Show more…

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Determine the domain of each function. $$ h(x)=\frac{x^{3}-64 x}{x^{2}+81} $$

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Key Concepts

Domain of a Function

The domain of a function refers to the set of all possible input values for which the function is defined. Determining the domain involves identifying values that may cause the function to be undefined, such as inputs that lead to division by zero, taking the square root of a negative number, or other undefined operations.

Rational Functions and Denominator Restrictions

A rational function is defined as the quotient of two polynomials. For these functions, the primary concern in determining the domain is ensuring that the denominator does not equal zero, since division by zero is undefined. This means that all values which make the denominator equal to zero must be excluded from the domain.

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