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)

If we assume you meant,

f(x) = 4^x/(4^x+2)

Then

f(1+x) = 4^1+x/(4^1+x+2)

= 4(4^x/(4(4^x)+2)

= 2(4^x/(2(4^x)+1)

= 2/(2+1/4^x)

= 2/(2+4^-x)

= 1 - f(-x)              

{ 1 - f(-x) = 1 - 4^-x/(4^-x+2) = 2/(2+4^-x) }

 

Regards,

Team,

TopperLearning.