If g(x) = ∫f(t)dt for t∈[1, x], then g(n) - g(1/n); n ∈ N is equal to (A) -1 (B) 1

Question

Let f be function satisfying the condition  f(xy) = f(x)/y + f(y)/x ∀ x, y > 0. If f(x) is differentiable and f(1) = 1, then

If g(x) = ∫f(t)dt for t∈[1, x],  then g(n) - g(1/n);  n ∈ N is equal to

(A) -1

(B) 1

(C) 0

(D) n + 1/n

Answer 1

Answer is (C) 0