CONTINOUS ON ENTIRE REAL LINE 

how do you solve it?

the function will be discontinuous if it is not at a particular pt. i.e. it becomes infinity or i.e. it has a break point.the above function can be written as as 1/e^z^4 .since exponential functions as always positive,and (also z^4 is positive) ,the denominator  never becomes zero n the funcction never becomes undefined or there is no break point.

z is a complex number....

sorry then ,coz they i dont know how to check its continuity on real line.