Let $A \subseteq (0, +\infty)$ be such that $\inf A=0$ and $A$ is NOT bounded from above. Find, if they exist, max, min, sup, inf of the set $$B=\bigg\{ \frac{x}{x+1}: x \in A \bigg\}.$$
I think that $$\sup B = 1, \space\inf B = 0,\space \nexists \max B,\space \nexists \min B$$
but I am not sure if it is right. Could you help me?
With your edit (the word NOT), your suggested answers look correct.
Clearly $0 \lt \frac{x}{x+1} \lt 1$ if $x$ is positive, and it approaches but does not achieve $0$ for very small $x$, and approaches but does not achieve $1$ for very large $x$