Question

Determine the domain of each function. $$ f(x)=\frac{x+7}{x^{3}+3 x^{2}-4 x-12} $$

Name: Problem 25, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2020-10-22T16:20:07-08:00
Duration: 1 min 7 s
Channel: Linh Vu
Description: Determine the domain of each function. f(x)=(x+7)/(x^3+3 x^2-4 x-12)

   Determine the domain of each function.
$$
f(x)=\frac{x+7}{x^{3}+3 x^{2}-4 x-12}
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 6, Problem 25

Instant Answer

Solved by Expert Linh Vu

10/22/2020

Step 1

The given function is a rational function, as it is a ratio of two polynomials. Show more…

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Determine the domain of each function. $$ f(x)=\frac{x+7}{x^{3}+3 x^{2}-4 x-12} $$

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Key Concepts

Domain of a Function

The domain of a function is the complete set of all possible input values (x-values) for which the function is defined. When determining the domain, special consideration is given to operations that may cause undefined expressions, such as division by zero or taking the square root of a negative number.

Rational Functions

Rational functions are expressions that represent the ratio of two polynomials, and their domains consist of all real numbers except those for which the denominator is zero. Identifying restrictions in the denominator is key in finding the domain of such functions.

Polynomial Factorization

Polynomial factorization involves breaking down a polynomial into simpler factors that, when multiplied together, yield the original polynomial. This technique is often used to identify the roots of the polynomial in the denominator of a rational function, which in turn helps determine the values that must be excluded from the domain.

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