Short Answer

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

The domain $(D_{f})$ of the function is the set of all real numbers $(x)$ such that $(x)$ belongs to real except 2.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. By definition of domain of a function.

The given function is $f (x) = \frac{1}{3 x - 6}$ . Now, by definition of domain of function, the domain of the function is defined for all real values of $(x)$ for which the function is defined.

Step 2. By definition of domain of rational function.

From the rational function $f (x) = \frac{1}{3 x - 6}$ , the domain is defined for all real numbers $(x)$ for which the denominator is non-zero.

$3 x - 6 \neq 0 gives x \neq 2$

Hence the domain of the function is $x \in R - {2}$

Step 3. Description of steps.

The domain of the function is $x \in R - {2}$ .

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Precalculus Mathematics for Calculus

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Short Answer

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

Step by Step Solution

Step 1. By definition of domain of a function.

Step 2. By definition of domain of rational function.

Step 3. Description of steps.

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