IIT JEE , AIEEE Forum - Mathematics , Algebra - functions-period

neeraj_agarwal_1990

Find period of

₄₂
e^cos^{x + x - [x] +cos}^{x

I've tried this..}since the numerator is positive(and not 0)...graph will be equivalent to that of e^xThus it has no period,domain is R and range is y>0

neeraj_agarwal_1990

Those missing objects are pie and 4 & 2 are powers of cos

sudeep.kumar

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.

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