(f∘g)(x) means f(g(x)) which means we substitute what g(x)
equals for x in the right side of f(x) if x appears in the right 
side of f(x).  If f(x) is a constant, it stays constant no matter
what x is.

on the interval where x < 0 f(x) is a constant function so
regardless of what g(x) is there, f(x) will be constantly 1. 

So the first part of (f∘g)(x) is (f∘g)(x) = 1 if x < 0


On the interval where , g(x) is 3x, so we substitute 3x
for x in that part of f(x), which is 2x² and get 2(3x)² or 2(9x²) or 18x².


So the second part of (f∘g)(x) is (f∘g)(x) = 18x² if 

on the interval where x > 1, f(x) is a constant function so
regardless of what g(x) is there, f(x) will be constantly 1.

So the third part of (f∘g)(x) is (f∘g)(x) = 1 if x > 1.

Therefore:

     

Edwin