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

Aug 5, 2015

Domain: $\left(- \infty , - 1\right) \cup \left(- 1 , + \infty\right)$
Range: $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

Explanation:

The domain of the function will have to take into account the fact that the denominator of the fraction cannot be equal to zero.

This means that any value of $x$ that makes the expression $x + 1 = 0$ will be excluded from the domain.

More specifically, you have

$x + 1 = 0 \implies x = - 1$

The domain of the function will thus be $\mathbb{R} - \left\{- 1\right\}$, or $\left(- \infty , - 1\right) \cup \left(- 1 , + \infty\right)$.

The range of the function will be influenced by the fact that you don't have a value of $x$ for which the function is equal to zero.

The range of the function will thus be $\mathbb{R} - \left\{0\right\}$, or $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$.

graph{1/(x+1) [-10, 10, -5, 5]}