Question

Find the domain of the function. $$f(x)=\frac{x+2}{x^{2}-1}$$

   Find the domain of the function.
$$f(x)=\frac{x+2}{x^{2}-1}$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 2, Problem 57

Instant Answer

Solved by Expert James Kiss

06/01/2020

Step 1

The function is defined for all real numbers except for the values of x that make the denominator equal to zero. Show more…

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Find the domain of the function. $$f(x)=\frac{x+2}{x^{2}-1}$$

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Key Concepts

Excluding Undefined Values

When determining the domain of a rational function, one must solve the equation set by equating the denominator to zero. The solutions to this equation are precisely the values that must be excluded from the domain, ensuring that every operation within the function is well-defined.

Domain

The domain of a function is the set of all input values for which the function is defined. In many cases, especially with real functions, this means identifying and excluding any numbers that lead to undefined operations, such as division by zero or taking the square root of a negative number.

Rational Functions

A rational function is expressed as the quotient of two polynomials. The important aspect when considering their domains is that any value of the variable that causes the denominator to be zero must be excluded, because division by zero is undefined in mathematics.

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