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Q56.

Expert-verifiedFound in: Page 157

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.

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.

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 $x\in R-\left\{2\right\}$

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

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