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  • DLS

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

Mathematics
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  • DLS
\[f(x)=\sin(\log(x-\sqrt{x^2+1}))\]
  • DLS
\[f(-x)=\sin(\log(\sqrt{x^2+1}-x)) \]
log (-A) is not -log A or log A so, its neither.

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Other answers:

  • DLS
its odd...
lets try an simplify x= tan y
  • DLS
rationalize..
  • DLS
kyun?
just rationalize f(-x).. you'll get to know why.
  • DLS
kyun karna hai?kaise pata chalega?
ye rd ka question hai. to mereko pta hai.. :P
you'll be using log (1/A) = - log A property here.
an sin(-t) = - sin t
  • DLS
ye to IIT ques hai..and why cant i see anyone viewing this question?
  • DLS
u cant either?
  • DLS
if I rationalize then how i am I using 1/logA property?
  • DLS
okay now i can see
  • DLS
people viewing
:/
what u got after rationalizing ?
  • DLS
\[\large x-\sqrt{x^2+1} \times \frac{x+\sqrt{x^2+1}}{{x+\sqrt{x^2+1}}}=\frac{1}{\sqrt{x^2+1}}\] hmm but how am i gonna think of this ?
  • DLS
misprint in = sorry :|
iit ka question hai mere bhai..
  • DLS
x+ also there
  • DLS
still :|
  • DLS
okay i have another doubt
  • DLS
\[\large \frac{1}{x+\sqrt{x^2+1}}\] =logA? logA to 1/x-sqrt{x^2+1} tha..minus tha :|
nhi.. galat hai method. pta nhi. :/
@hartnn ? :O
what ?
dls's last post. rationalizing wont work.
it does ?
rationalizing changes middle sign :\]
we'll get log(x+ sqrt(x^2+1)) right? but f(x) is..... exactly...
  • DLS
dafuq :|
  • DLS
@yrelhan4 RD khol
yr dusre room me padi hai. :/
  • DLS
ja na please :| mere solution me usse (a+b)(a-b) ka use kara hai..why :/
  • DLS
\[\LARGE \sin(\log(\frac{1}{x+\sqrt{x^2+1}}))=\sin(\log1-\log(x+\sqrt{x^2+1}\] ..done

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