FunctionMedium
Question
Let g(x) = log(f(x)) where f(x) is a twice differentiable positive function on (0, ∞) such that f(x + 1) = x f(x). Then, forN = 1, 2, 3,......g″ 
=
=Options
A.
B.
C.
D.
Solution
g(x + 1) = log(f(x + 1)) = logx + log(f(x)) = logx + g(x)
⇒ g(x + 1) - g(x) = logx
⇒ g″(x + 1) - g″(x) = -
= - 4
......
......
Summing up all terms
Hence,
⇒ g(x + 1) - g(x) = logx
⇒ g″(x + 1) - g″(x) = -
= - 4......
......
Summing up all terms
Hence,
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