sir , can you please help me solving this question :- Q:-If the function f:R->R defined by f(x)=4^x/4^x+2 , then show that f(1+x)=1-f(x)

Asked by Bharadwaj.R.S | 6th Aug, 2010, 12:00: AM

Expert Answer:

If we assume you meant,
f(x) = 4x/(4x+2)
Then
f(1+x) = 41+x/(41+x+2)
= 4(4x/(4(4x)+2)
= 2(4x/(2(4x)+1)
= 2/(2+1/4x)
= 2/(2+4-x)
= 1 - f(-x)              
{ 1 - f(-x) = 1 - 4-x/(4-x+2) = 2/(2+4-x) }
 
Regards,
Team,
TopperLearning.

Answered by  | 6th Aug, 2010, 09:41: PM

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