Calculus: Chain Rule

Suppose the functions f(x) and g(t) are defined as follow:
f(x) =
6x, x ≥ 0
2x^2, x < 0

g(t) =
3t; t ≤ 0
t2; t > 0

a. Show that (g o f)(x) will be given by:

(g o f)(x) =
36x2, x ≥ 0
4x4, x < 0

I am so confused on how to do this problem. If you could please show me the steps to do this problem.

Note : g(t) = t², ... if t > 0.
________________________

If x ≥ 0, then ƒ(x) = 6x ≥ 0.

∴ (goƒ)(x) = g(ƒ(x)) = g(6x) = (6x)² = 36x² ...... (1)
______________________

If x < 0, then : ƒ(x) = 2x² > 0.

∴ (goƒ)(x) = g(ƒ(x)) = g(2x²) = (2x²)² = 4x⁴ ...... (2)
_______________________

∴ from (1) and (2) :

g(x) = 36x², ............... if x ≥ 0

. . . .= 4x⁴, ................ if x < 0.
________________________