MathDB

Let function pair

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

satisfies

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

for every

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

a. Prove that

f(x) = 2015g(x)

for every

x \in \mathbb{R^+}

b. Give an example of function pair

(f,g)

that satisfies the statement above and

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

for every

x \in \mathbb{R^+}

4