Therefore: t≥-5/4

Therefore: f[g(x)]=f(t)=-t? -t=-(t+ 1/2)？ +1/4, axis of symmetry t=- 1/2.

Combined image

When t≥-5/4, f[g(x)]=f(t)=-t? -t=-(t+ 1/2)？ +1/4 gets the maximum value of 1/4.

Therefore, the range of f[g(x)] is (-∞, 1/4).