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f(x)=log(x+(x2+1)1/2) is (a) even function (b) odd fubction (c)periodic function (d)neither even nor odd function

Explain ur answer pls.

Aditi Bhatnagar , 14 Years ago
Grade 12th Pass
anser 1 Answers
Ashwin Muralidharan IIT Madras

Hi Aditi,

 

Note that √(x2+1) - x = 1/[√(x2+1) + x]

Hence log(√(x2+1) - x) = -log[√(x2+1) + x]

 

Hence f(-x) = -f(x).

Hence f(x) is odd.

 

Hope that helps.

 

Best Regards,

Ashwin (IIT Madras).

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