> 
> Let $f :\mathbb R \rightarrow\mathbb R$ be continuous function . Then which cannot be the image of $(0,1]$ ?
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> A. $\{0\}$
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> B. $(0,1)$
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> C. $[0,1)$
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> D. $[0,1]$
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> 

Now A. is the constant map. C. is the map $f(x)=1-x$.
Little confusion about B. and D. If it is that $(0,1)$ is embedded in $(0,1]$ so B. cannot be the answer then similarly $(0,1]$ is embedded in $[0,1]$ so D. is also not the answer . All answers wrong is not a possibility. What did I miss here?