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Is the pair of the functions e^(sqrt(log...

Is the pair of the functions `e^(sqrt(log_(e)x))` and `sqrt(x)` identical ?

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`e^(sqrt(log_(e)x))=(e^(logx))^((1)/(2))=sqrt(x)=sqrt(x), " where " x ge 1`
For `sqrt(x),x ge0,`
Thus, functions are not identical as domain is not same.
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