DLS
Test whether the following function is odd/even/either/neither



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\[f(x)=\sin(\log(x\sqrt{x^2+1}))\]

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\[f(x)=\sin(\log(\sqrt{x^2+1}x)) \]

hartnn
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log (A) is not log A or log A
so, its neither.

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its odd...

hartnn
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lets try an simplify
x= tan y

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@yrelhan4

yrelhan4
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rationalize..

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kyun?

yrelhan4
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just rationalize f(x).. you'll get to know why.

DLS
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kyun karna hai?kaise pata chalega?

yrelhan4
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ye rd ka question hai. to mereko pta hai.. :P

hartnn
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you'll be using log (1/A) =  log A property here.

hartnn
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an sin(t) =  sin t

DLS
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ye to IIT ques hai..and why cant i see anyone viewing this question?

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u cant either?

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if I rationalize then how i am I using 1/logA property?

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okay now i can see

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people viewing

yrelhan4
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:/

hartnn
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what u got after rationalizing ?

DLS
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\[\large x\sqrt{x^2+1} \times \frac{x+\sqrt{x^2+1}}{{x+\sqrt{x^2+1}}}=\frac{1}{\sqrt{x^2+1}}\]
hmm but how am i gonna think of this ?

DLS
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misprint in = sorry :

yrelhan4
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iit ka question hai mere bhai..

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x+ also there

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still :

DLS
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okay i have another doubt

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\[\large \frac{1}{x+\sqrt{x^2+1}}\]
=logA? logA to 1/xsqrt{x^2+1} tha..minus tha :

yrelhan4
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nhi.. galat hai method. pta nhi. :/

yrelhan4
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@hartnn ? :O

hartnn
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what ?

yrelhan4
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dls's last post. rationalizing wont work.

hartnn
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it does ?

hartnn
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rationalizing changes middle sign :\]

yrelhan4
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we'll get log(x+ sqrt(x^2+1)) right?
but f(x) is.....
exactly...

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dafuq :

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@yrelhan4 RD khol

yrelhan4
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yr dusre room me padi hai. :/

DLS
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ja na please :
mere solution me usse
(a+b)(ab) ka use kara hai..why :/

DLS
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\[\LARGE \sin(\log(\frac{1}{x+\sqrt{x^2+1}}))=\sin(\log1\log(x+\sqrt{x^2+1}\]
..done