Sets and Relation problem

Question

Domain of !!f(x) = log(cosx)!!

!!a)" "[ 2npi - pi/2 , 2npi + pi/2 ]!!

!!b)" "( 2npi - pi/2 , 2npi + pi/2 )!!

!!c)" "!!None

Solution

In the given function !!f(x) = log(cosx)!! we know that the range of !!cosx!! is from !![-1,1]!!.

But the value of !!A!! in !!logA!! can not be negative or zero. Considering this in mind we can only have positive values of !!cosx!!.

We know that range of !!cosx!! remain positive only in !!1st and 4th!! quadrant in !!x-y!! axis.

Hence domain of !!f(x) = log(cosx)!! should lie between !!( 2npi - pi/2 , 2npi + pi/2 )!!

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