Question

Find the domain of the function. $$f(x)=\frac{1}{3 x-6}$$

   Find the domain of the function.
$$f(x)=\frac{1}{3 x-6}$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 2, Problem 56

Instant Answer

Solved by Expert James Kiss

06/01/2020

Step 1

The given function is \( f(x) = \frac{1}{3x - 6} \), which is a rational function. A rational function is defined for all real numbers except where the denominator is zero. Show more…

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Find the domain of the function. $$f(x)=\frac{1}{3 x-6}$$

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Key Concepts

Domain of a Function

The domain of a function is the set of all input values (typically real numbers) for which the function is well-defined. Determining the domain involves identifying any restrictions that would lead to undefined operations, such as division by zero or taking even roots of negative numbers in the context of real-valued functions.

Rational Functions and Division by Zero

Rational functions are functions represented by the ratio of two polynomials. A critical aspect of analyzing rational functions involves finding the values for which the denominator is zero, as these values must be excluded from the domain. This is because division by zero is undefined in mathematics, making such input values invalid.

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