$A:=\{f(x) : x \in [1,2]\} \cup \{x:x\in[1,2]\}$ where $f:[0,4]\to\Bbb R$ given by $f(x):=x^2+2$ for all $x \in [0,4]$.
My working: the range of $f$ is $f([1,2]) = [3,6]$, and $x:x\in[1,2]$ gives $[1,2]$, so $[3,6]\cup[1,2]$.
I know this means that $1\leq x\leq2$ or $3\leq x\leq6$. Does that mean I write $A:=[1,2]\cup[3,6]$? and that is fine to write and fully simplified. Also, out of interest, would the supremum of $A$ be $6$ and infimum be $1$?