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Question

The domain of fx=cot-1xx2-x2, xR is


A

R

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B

R-0

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C

R-±n,n0,Z

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D

None of these

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Solution

The correct option is C

R-±n,n0,Z


Explanation for the correct option :

Find the domain of fx,

Consider the given Equation as,

fx=cot-1xx2-x2

In the above Equation under root

x2-x2>0x2-x2>0

Since xI then x=x

If x2R-I, then x2I

Then, x2>x2

x2=R-0,±1,±2,±4......x2=R-0,1,2,3,4......x=R-0,1,2,3,4.........nx=R-±n,n0,nz

Hence, the correct answer is Option (C).


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