Dear Neeraj,

 

You are missing somethng here...

 

The function is e^ cos(pix)   and cos function is periodic and not strictly increasing as x and hence you cant compare this function with e^x.

 

Now the solution....

 

Period of even power of sin and cos is pi,

and so, period of  even powers of cos (pi)x is 1.

 

also,  x - [x] = {x} , and period of {x} is also 1.

 

So, the period of the given function is 1.