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f(x)=log(x+(x 2 +1) 1/2 ) is (a) even function (b) odd fubction (c)periodic function (d)neither even nor odd function Explain ur answer pls.

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.

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

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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