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anurag singhal Grade:
        

log10log2log2/pi(tan-1x)-1

8 years ago

Answers : (1)

askIITianexpert IITDelhi
8 Points
										

Every base in above expression is +ve & not equal to 1 so that part of the requirement is fulfilled.


For tan-1x to be defined x could take any real value.


For (tan-1x)-1 to be defined x could take any real value except where tan-1x=0 ;i.e. x ≠0.


For log2/pi(tan-1x)-1 to be defined (tan-1x)-1 >0 ;i.e. x>0.


For log2log2/pi(tan-1x)-1  to be defined  log2/pi(tan-1x)-1 >0;or,(tan-1x)-1 >1;or, tan-1x<1;or,x<tan(1 radian).


At last for log10log2log2/pi(tan-1x)-1 to be defined log2log2/pi(tan-1x)-1 >0;or, log2/pi(tan-1x)-1 >1


or, (tan-1x)-1 <2/pi                 ....[coz' (2/pi)<1]


or, tan-1x>pi/2 which couldn't be possible for any real x.    ---[-¶/2≤tan-1x¶/2;principal values.]


Hence the given expression is not defined for any x or it's domain is a null set.


This could be easily deducted by doing last step first & such kind of intution could be mastered by good practice.I just give these steps for the thoroughness.

8 years ago
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