FunctionHard

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,

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