數學Question (10P)

If x＜0, f o g(x) = f(g(x)) = f(2) = 1

【If 0≦x≦1, f o g(x) = f(3x)】
(Since 0≦3x≦3, we need to split this case further. This part should not be shown in your work. I include it here just because I want to let you know why I should split the cases in the following way)

if 0≦x≦1/3, then 0≦3x≦1, f o g(x) = f(3x) = (3x)^2 = 9x²

if 1/3＜x≦1, then 1≦3x, f o g(x) = f(3x) = 1

If 1＜x, f o g(x) = f(g(x)) = f(2) = 1

Therefore, in summary,
f o g(x) = {1, if x＜0 or x＞1/3} {9x², if 0≦x≦1/3}