Question 61
The continuous functions $f, g: [0, \infty) \to [0, \infty)$ have the properties:
(i) $f(0) = g(0) = 0$;
(ii) $g(x) \neq 0$, for every $x \gt 0$;
(iii) $f(x + g(f(x))) = f(x)$, for every $x \ge 0$.
Show that $f(x) = 0$, for every $x \ge 0$.
(i) $f(0) = g(0) = 0$;
(ii) $g(x) \neq 0$, for every $x \gt 0$;
(iii) $f(x + g(f(x))) = f(x)$, for every $x \ge 0$.
Show that $f(x) = 0$, for every $x \ge 0$.