Question 2
(CHN 1) Let $\mathbb R^+$ be the set of all nonnegative real numbers. Given two positive real numbers $a$ and $b$, suppose that a mapping $f:\mathbb R^+\to\mathbb R^+$ satisfies the functional equation
$$f(f(x))+af(x)=b(a+b)x.$$
Prove that there exists a unique solution of this equation.
$$f(f(x))+af(x)=b(a+b)x.$$
Prove that there exists a unique solution of this equation.