Let, $A=f(B)\subset \mathbb R$ ,where $B$ is closed interval contained in $(0,\infty)$ and $f(t)=\log t$. Then $A$ is
(d) connected ?
Clearly $f$ is continuous. Suppose that $B=[a,b]\subset(0,\infty)$. Then $B$ is connected & so $A=f(B)$ is connected.
As any closed interval in $\mathbb R$ is closed & bounded so, compact & hence $A$ is compact. Continuous image of open or closed set is not necessarily open or closed.
So options (c) & (d) are correct. But the answer is given (a) & (d).
Where my mistake?