# Domain of 2 Functions in a Max()

let $f(x) = x^3 \in [-2,5]$

$g(x) = \max(f(x), f(x-1))$

How do I find the domain for $g(x)$?

I believed that the domain was still $[-2, 5]$, because $f(x) > f(x-1)$

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Is $x^3 \in [-2,5]$ or $x \in [-2,5]$? –  Henry Jan 12 '12 at 23:27
You will have problems calculating $g(-1.25)$ and some other cases. –  Henry Jan 12 '12 at 23:29
The domain of $\max(f,h)$ is the intersection of the domain of $f$ and the domain of $h$. However, I am confused about why $x^3$ should have domain $[-2,5]$. It seems to be defined on all of $\mathbb{R}$.