# How do you find the domain of f(x)=x^3-8x+4?

Jun 14, 2018

$x \in \mathbb{R}$

#### Explanation:

We're dealing with a polynomial here, which is defined for all real numbers. Let's think for a moment:

Are there any values of $x$ that will make my function undefined?

Let's plug in some values for $x$:

$f \left(3\right) = {\left(3\right)}^{3} - 8 \left(3\right) + 4 = \textcolor{b l u e}{7}$

$f \left(11\right) = {\left(11\right)}^{3} - 8 \left(11\right) + 4 = \textcolor{b l u e}{1247}$

$f \left(41\right) = {\left(41\right)}^{3} - 8 \left(41\right) + 4 = \textcolor{b l u e}{68597}$

Notice, I could have picked much more ridiculous values for $x$, but we see that it is defined for all real numbers. We can say

$x \in \mathbb{R}$

Hope this helps!