# How do you find the domain of f(x)=e^x - 6?

May 24, 2017

Domain: All $x$ that are in $\mathbb{R}$ (set of real numbers)

#### Explanation:

The domain of a function is essentially asking what are the "legal" values of $x$ you can plug in and get a result. The way to do this is to find all the "Illegal" values of $x$ and then exclude those from the result.

Domain: All $x$, except for these illegal ones.

Illegal values are values that would make you divide by zero, or would result in negatives under square roots. In this function, there are no values that would make you divide by zero. There are also no roots, so there is no risk of getting a negative value under a root.

So there are no "illegal" values of $x$

Domain: All $x$ that are in $\mathbb{R}$ (set of real numbers)