# What is the domain and range of y=1/(x-4)?

Jul 13, 2016

This is a Rational Function.
Rational Function is undefined when denominator becomes zero.
$\implies$ y is undefined when denominator $x - 4 = 0$.
$\implies$ y is undefined when denominator $x = 4$.

$\implies$ This function is defined for all real numbers except 4.
$\implies$ Domain$= \mathbb{R} - \left\{4\right\}$

This function can have any real value except zero.
$\implies$ Range$= \mathbb{R} - \left\{0\right\}$

Where $\mathbb{R}$ is set of all real numbers.