Question 989649
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f(x) = {{{(-0.25 + e^x)^(1/2)}}}.


I corrected your writing. 
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Your function is  f(x) = {{{sqrt(e^x-0.25)}}}.


Notice that  {{{e^x}}}  is  1  at  x=0.


Your function is continuous from both sides at 0, continuous from the left at 0, and continuous from the right at 0.