Question

if func f(x) satisfies the relation
f(x+y)=y|x-1|/(x-1)*f(x) + f(y) with f(1)=2 then

Answer 1

find

Answer 2

\[\lim_{x \rightarrow 1}f'(x)\]

Answer 3

@LastDayWork any idea??

Answer 4

@ganeshie8

Answer 5

My answer -
Zero

Solution
\[f(x+y) = y \frac{ |x-1| }{ x-1 }f(x) + f(y)\]
substituting x = 0 ; y = 1
f(1) = -f(0) + f(1)
implies f(0) = 0

\[f(x+y) = y \frac{ |x-1| }{ x-1 }f(x) + f(y)\]
substituting y = 0
f(x) = f(0) = 0

Hence,
f(x) = 0 ; for x ≠ 1
f(x) = 2 ; for x = 1