# How do you find the domain and range of g(x)=1/(x+1)?

Jul 13, 2016

This is a Rational Function.
Rational Function is undefined when denominator becomes zero.
$\implies$ g(x) is undefined when denominator $x + 1 = 0$.
$\implies$ g(x) is undefined when denominator $x = - 1$.

$\implies$ This function is defined for all real numbers except $- 1$.
$\implies$ Domain$= \mathbb{R} - \left\{- 1\right\}$

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.

Jul 13, 2016

This is a Rational Function.
Rational Function is undefined when denominator becomes zero.
$\implies$ y is undefined when denominator $x + 1 = 0$.
$\implies$ y is undefined when denominator $x = - 1$.

$\implies$ This function is defined for all real numbers except $- 1$.
$\implies$ Domain$= \mathbb{R} - \left\{- 1\right\}$

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.