MathDB

Let functions

f, g: \mathbb{R}^+ \to \mathbb{R}^+

satisfy the following:

f(g(x)y + f(x)) = (y+2015)f(x)

for every

x,y \in \mathbb{R}^+

. (a) Prove that

g(x) = \frac{f(x)}{2015}

for every

x \in \mathbb{R}^+.

(b) State an example of function that satisfy the equation above and

f(x), g(x) \ge 1

for every

x \in \mathbb{R}^+

A6