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

Aug 16, 2015

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

#### Explanation:

Your function is defined for any value of $x$ except the value that will make the denominator equal to zero.

More specifically, your function $\frac{1}{x}$ will be undefined for $x = 0$, which means that its domain will be $\mathbb{R} - \left\{0\right\}$, or $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$.

Another important thing to notice here is that the only way a fraction can be equal to zero is if the numerator is equal to zero.

Since the numerator is constant, your fraction has no way of ever being equal to zero, regardless of the value $x$ takes. This means that the range of the function will be $\mathbb{R} - \left\{0\right\}$, or $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$.

graph{1/x [-7.02, 7.025, -3.51, 3.51]}