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ISI 2018 #4

Source: ISI 2018 B.Stat / B.Math Entrance Exam

May 13, 2018
isi2018Indian Statistical Institutecalculus

Problem Statement

Let f:(0,∞)→Rf:(0,\infty)\to\mathbb{R} be a continuous function such that for all x∈(0,∞)x\in(0,\infty), f(2x)=f(x)f(2x)=f(x) Show that the function gg defined by the equation g(x)=∫x2xf(t)dtt  for x>0g(x)=\int_{x}^{2x} f(t)\frac{dt}{t}~~\text{for}~x>0 is a constant function.
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