if e to the power f(x)=(10+x) / (10-x) ,x belongs to (-10,10) and f(x)=k f((200x) / (100+x^2)) , then k=

please can u show each step to solve this problem immediately

thanks in advance.

Question

if e to the power f(x)=(10+x) / (10-x) ,x belongs to (-10,10)
and f(x)=k f((200x) / (100+x^2)) , then k=
please can u show each step to solve this problem
immediately
thanks in advance

Vipin Verma · Accepted Answer

ef(x) =10+x10-xTaking log on both sides, we havef(x) =
log[10+x10-x] (1)And f(x) =kf(200x100+x2)Put x =200x100+x2 in (1) ,
we have f(200x100+x2) =log[10+200x100+x210-200x100+x2]
=log[1000+10x2 +200x1000+10x2-200x] (2)As f(x) =kf(200x100+x2)So
using (1) and (2) , we have log[10+x10-x] =klog[1000+10x2
+200x1000+10x2-200x] So k = log[10+x10-x] log[1000+10x2
+200x1000+10x2-200x] (3)As x lies between (-10 , 10)So put x = 1,
in (3) , you will get log(11/9)log(121/81) =log(11/9)2log(11/9) =
1/2 Put x = 2, you will get log(12/8)log(144/64)
=log(12/8)2log(12/8) = 1/2put x = -3 , you will get k = 1/2Hence k
= 1/2 for x belongs to (-10 ,10)

if e to the power f(x)=(10+x) / (10-x) ,x belongs to (-10,10) and f(x)=k f((200x) / (100+x^2)) , then k= please can u show each step to solve this problem immediately thanks in advance.

if e to the power f(x)=(10+x) / (10-x) ,x belongs to (-10,10) and f(x)=k f((200x) / (100+x^2)) , then k=

please can u show each step to solve this problem immediately

thanks in advance.