+776 Make sure that x^3 + 4 is not 0. Dividing by 0 is undefined. This means that \(x^3 \ne -4 \Rightarrow x \ne ^3\sqrt{-4} \Rightarrow x \ne 2i\).
This value is not real, so we do not need to consider it. The domain of \(f(x) = \dfrac{6x}{x^3+4}\) is \(x \in (-\infty, \infty)\).
- PM
+776 Actually, I think \(^3\sqrt-4\) might actually be a real number, so the domain is \(x \in (-\infty, ^3\sqrt-4) \cup (^3\sqrt-4, \infty)\).
+130077 y = 6x / [ x^3 + 4]
The domain will only be affected by any x that makes the denominator = 0
So....set the denominator to 0 to find this value
x^3 + 4 = 0
x^3 = -4 take the cube root of both sides
x = ∛-4 = - ∛4
So....the domain is
(-infinity, -∛ 4 ) U ( - ∛4, infinity )
Here's a graph : https://www.desmos.com/calculator/qih0ucpatr
