Quote:
Originally Posted by lime
Hi! That is really buffling question for me as well, but I cannot understand another variant:
*by the way the question was about (0,1) not [0,1].
WHY? If f=tan(Pi/2*(x-0.5)) so in that case we have (0,1)->(-inf, +inf) and it is not bounded? Where am I wrong? 
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lime, (0,1) doesnt map to (-inf,+inf) with that function. the range is (-inf,1). Substitute x=1 and you will get f= tan (pi/2*1/2)= tan (pi/4)=1.