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  • Which of the following is an odd function?Option: 1 <img alt="\log(x+\sqrt{x^2-1})" src="https://learn.careers360.com/latex-image/?%5Clog%28x&plu

Which of the following is an odd function?

Option: 1

\log(x+\sqrt{x^2-1})


Option: 2

log x


Option: 3

e^x


Option: 4

10^x


Answers (1)

best_answer

If f(x)= \log (x+\sqrt{x^2-1})

f(-x)= \log (-x+\sqrt{x^2-1})=\log \left [(-x+\sqrt{x^2-1})\times \frac{(x+\sqrt{x^2-1})}{x+\sqrt{x^2-1}} \right ]

=\log\frac{1}{(x+\sqrt{x^2-1})}= -log (x+\sqrt{x^2-1}) = -f(x)

Hence it is an odd function

Posted by

shivangi.shekhar

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