## DLS 2 years ago Test whether the following function is odd/even/either/neither

1. DLS

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

2. DLS

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

3. hartnn

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

4. DLS

its odd...

5. hartnn

lets try an simplify x= tan y

6. DLS

@yrelhan4

7. yrelhan4

rationalize..

8. DLS

kyun?

9. yrelhan4

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

10. DLS

kyun karna hai?kaise pata chalega?

11. yrelhan4

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

12. hartnn

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

13. hartnn

an sin(-t) = - sin t

14. DLS

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

15. DLS

u cant either?

16. DLS

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

17. DLS

okay now i can see

18. DLS

people viewing

19. yrelhan4

:/

20. hartnn

what u got after rationalizing ?

21. 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 ?

22. DLS

misprint in = sorry :|

23. yrelhan4

iit ka question hai mere bhai..

24. DLS

x+ also there

25. DLS

still :|

26. DLS

okay i have another doubt

27. DLS

$\large \frac{1}{x+\sqrt{x^2+1}}$ =logA? logA to 1/x-sqrt{x^2+1} tha..minus tha :|

28. yrelhan4

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

29. yrelhan4

@hartnn ? :O

30. hartnn

what ?

31. yrelhan4

dls's last post. rationalizing wont work.

32. hartnn

it does ?

33. hartnn

rationalizing changes middle sign :\]

34. yrelhan4

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

35. DLS

dafuq :|

36. DLS

@yrelhan4 RD khol

37. yrelhan4

yr dusre room me padi hai. :/

38. DLS

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

39. DLS

$\LARGE \sin(\log(\frac{1}{x+\sqrt{x^2+1}}))=\sin(\log1-\log(x+\sqrt{x^2+1}$ ..done