分からない問題はここに書いてね445

Let f ： X → Y and g ： Y → Z
Let x_0 be a limit point of X and
let y_0 be a limit point of Y

Consider the following three conditons:

(i) f(x) → y_0 as x → x_0
(ii) g(y) → z_0 as y → y_0
(iII) g(f(x)) → z_0 as x → x_0

(b) Show that if (i) and (ii) hold and if g(y_0) = z_0, then (iii) holds.