Suppose $f$ is defined on $[0;4]$ and $g(x) = f(x+3)$ what is the domain of $g$?
I'm having a tough time solving this problem. I know that $0 \leq x \leq 4$ for the domain of $f$. So would it be correct to say that for the function $g$, $0 \leq x +3\leq 4$ so:$$f(0) \leq f(x+3) \leq f(4)$$ $$ \Rightarrow f(0) \leq g(x) \leq f(4)$$
I'm not sure how to proceed. A little assistance would be greatly appreciated.