1. what is period of f(x)=|tanx| + cos 2x ?

2. what is period of function f(x)= log arcsin({x}),here {.} is fractional part function.plzzz do graphically .

Hi Manuj,

1. The period of |tanx| = pi.

As |tan(x+pi)| = |tanx|.

So its period is pi.

And the period of cos2x is (2pi)/2 -------(As period of cosax = (2pi)/|a|).

Hence the period of |tanx| + cos2x is pi.

Hope this helps.

Wish you all the best.

Regards,

Ashwin (IIT Madras).

Hi Manuj,

2. This question involves only drawing the graph of {x}.

As {x} is periodic with period of 1, so any function g({x}) will be periodic with period of 1.

Hence the period of the second question is 1.

_{/ / / / / / / / / / / / /} (This represents the graph of {x})

^{012345678............} (represents the points along the x-axis).

Hope it helps.

Wish you all the best.

Regards,

Ashwin (IIT Madras).

in first question f(x) is even function. therefore period should be equaL to 1/2 L.C.M of {t1,t2}.therefore period must be equal to pi/2.

Hi Manuj,

It is not about f(x) being exen in this case.

You can clearly see that pi/2 is not the period of this function.

It will remanin pi only.

As |tanx| and cos2x do not complement each other for pi/2.

(For detailed explanation on this, refer your period-2 Question).

With Regards,

Ashwin (IIT Madras).