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Found in: Page 157

### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

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

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

See the step by step solution

## Step 1. By definition of domain of a function.

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

## Step 2. By definition of domain of rational function.

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

$3x-6\ne 0\text{\hspace{0.17em}gives}\phantom{\rule{0ex}{0ex}}x\ne 2$

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

## Step 3. Description of steps.

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