To expand the function f(x) = (x^2 - 2x - 3)^2, we need to first expand the inner polynomial (x^2 - 2x - 3) using the distributive property for squaring binomials:

(x^2 - 2x - 3)^2
= (x^2 - 2x - 3)(x^2 - 2x - 3)
= x^4 - 2x^3 - 3x^2 - 2x^3 + 4x^2 + 6x - 3x^2 + 6x + 9
= x^4 - 4x^3 - 2x^2 + 4x + 9

Therefore, the expanded form of the function f(x) = (x^2 - 2x - 3)^2 is f(x) = x^4 - 4x^3 - 2x^2 + 4x + 9.