Question

Find the domain of $f(x)=\frac{x+3}{x^{2}+2 x-8}$

   Find the domain of $f(x)=\frac{x+3}{x^{2}+2 x-8}$

Algebra and Trigonometry

Algebra and Trigonometry

Michael Sullivan 11th Edition

Chapter 6, Problem 34

Instant Answer

Solved by Expert Kimberly Waterbury

07/02/2021

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The denominator of the function is $x^{2}+2x-8$. Show more…

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Find the domain of $f(x)=\frac{x+3}{x^{2}+2 x-8}$

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Key Concepts

Denominator Restrictions

In rational functions, the denominator cannot be zero because division by zero is undefined in mathematics. Thus, determining the domain involves finding the values that cause the denominator to equal zero and excluding them from the set of possible inputs.

Polynomial Factoring

Polynomial factoring is a technique used to simplify polynomials by expressing them as a product of their factors. When dealing with rational functions, factoring the denominator can reveal the values that make the denominator zero, which are then excluded from the domain.

Domain

The domain of a function refers to the set of all possible input values (typically x-values) for which the function is defined. For most functions, especially rational functions, identifying the domain involves determining which x-values might lead to undefined expressions such as division by zero or negative values under an even root.

Rational Functions

Rational functions are functions that can be expressed as the ratio of two polynomials. They are subject to restrictions that arise from the denominator since any value that zeroes the denominator must be excluded from the domain to avoid undefined behavior.

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