sir , i tried hard to solve this question but im unable to continue .can u please help me solving it :- Question:-If f:R-{+or-}->R is defined by f(x)=log|1+x/1-x| , then show that f(2x/1+x^2)=2f(x)

Asked by Bharadwaj.R.S | 1st Aug, 2010, 12:00: AM

Expert Answer:

Dear Student,
 
Let us substitute x=tany.
So, f(2x/1+x2) can be rewritten as:
 
      f(2tany/1+tan2y)
=>  f(sin2y)
So, to prove is;
f(sin2y) = 2f(tany)............(1)
 
Now, taking LHS of equation (1):
 
=> f(sin2y)
=> log|1+sin2y/1-sin2y|.......................[f(x)=log|1+x/1-x|]
=> log|(1+tan2y+2tany)/(1+tan2y-2tany)|
=> log [(1+tany)2/(1-tany)2]
=> 2log[(1+tany)/(1-tany)]
=> 2f(tany)
=> RHS of equation (1)
Hence Proved
Regards Topperlearning.

Answered by  | 1st Aug, 2010, 10:57: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.