# What is the domain and range of f(x)= 1/(x+1)?

Aug 3, 2015

$x \ne - 1 \mathmr{and} y \ne 0$

#### Explanation:

If $x = 1$ the denominator of the fraction would be $= 0$ which is not allowed.
If $x$ becomes larger the function would get nearer to $0$ without getting there.

Or, in "the language":

${\lim}_{x \to - 1 +} f \left(x\right) = \infty \mathmr{and} {\lim}_{x \to - 1 -} f \left(x\right) = - \infty$

${\lim}_{x \to \pm \infty} f \left(x\right) = 0$
graph{1/(x+1) [-10, 10, -5, 5]}