The function defined by f(x) is

To determine the properties of f(x) = 2x^3 - 15x^2 + 36x + 1 on [0, 3], first compute the derivative: f'(x) = 6x^2 - 30x + 36 = 6(x-2)(x-3). The critical points are x=2 and x=3. Testing intervals shows f'(x) > 0 for x in [0, 2) and f'(x) < 0 for x in (2, 3). Since the function increases then decreases, it is not monotonic and therefore not injective. Evaluating key points: f(0) = 1, f(2) = 29, and f(3) = 28. The range is [1, 29], which matches the given codomain. Thus, the function is surjective but not injective.