Final answer:
The domain of the function f(x) = 10ˣ² + log(1 - 2x) is all real numbers less than 0.5, which is expressed mathematically as x ∈ (-∞, 0.5).
Step-by-step explanation:
To find the domain of the function f(x) = 10ˣ² + log(1 - 2x), we need to consider the properties of the functions involved, namely the exponentiation and the logarithm. The term 10ˣ² does not impose any restrictions on x, as any real number squared is valid. However, the logarithmic part, log(1 - 2x), requires the argument (1 - 2x) to be positive, since the logarithm of a non-positive number is undefined. This gives us the inequality 1 - 2x > 0. Solving this inequality, we find that x < 0.5. Therefore, the domain of the function is all real numbers less than 0.5: x ∈ (-∞, 0.5).