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Question

The function fx=seclogx+1+x2 is


A

Odd

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B

Even

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C

Neither odd nor even

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D

Constant

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Solution

The correct option is B

Even


Explanation for correct answer

We know that in even function fx=f-x

fx=seclogx+1+x2

f-x=seclog-x+1+-x2=seclog1+x2-x=seclog1+x2-x1+x2+x1+x2+x=seclog1+x2-x21+x2+x=seclog11+x2+x=seclog1-log1+x2+xlogab=loga-logb=sec-log1+x2+xlog1=0=seclog1+x2+xsec-θ=secθ

Therefore fx=f-x, so, the function is even.

Hence, OptionB is correct.


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