The function f(x) = log (x + \sqrt{x^2+1}) is

Correct Answer is : an odd function

Neither an even nor an odd function

NIMCET 2018 Question Paper with solutions

Question : 37 of 120

Marks: +1, -0

The function f(x) = log (x +

√{x^2+1}

) is

Solution:

Given that,
f(x) = log (x +

√{x^2+1}

)
∴ f (-x) = log (- x +

√{x^2+1}

)
= log

({√{x^2+1}-x}/1×{√{x^2+1}+x}/{√{x^2+1}+x})

[by rationalisation]
= log

({x^2+1-x^2}/{√{x^2+1}+x})

log

(x + √{x^2+1})^{-1}

= - log (x +

√{x^2+1}

)
f (-x) = - f (x)
Hence, f(r) is an odd function.

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