Final answer:
To unambiguously represent the signal given by the function x(t), the minimum sampling frequency must be at least twice the highest frequency component of the signal, which means it must be at least 450 Hz.
Step-by-step explanation:
The signal x(t) provided in the question is a composite signal consisting of a constant component and two cosine functions with different frequencies. The frequencies of these cosine functions (75 Hz and 225 Hz) represent the highest frequency component of the signal. According to the Nyquist Theorem, the minimum sampling frequency (fs) necessary to avoid ambiguity and aliasing in the sampled signal must be at least twice the maximum frequency present in the signal. Therefore, for the signal x(t) = 4.0 + 2.0cos(150πt) + 1.0cos(450πt+π/2), the highest frequency is 225 Hz, which gives us an fs of at least 2 × 225 Hz, which is 450 Hz.