Final answer:
The function f(x) = (2x-3)((x²-1)(x+2)) is a polynomial, which is typically defined for all real numbers and does not become undefined at any of the given options.
Step-by-step explanation:
To find the value of x for which the function f(x) is undefined, we need to look for any restrictions in the domain of f(x). Since f(x) is a polynomial function and does not have any rational expressions or radicals, it is typically defined for all real numbers. However, the question provides the function in a factored form: f(x) = (2x-3)((x²-1)(x+2)). The factors (x²-1) and (x+2) suggest roots, but they do not cause f(x) to be undefined. The only way f(x) could become undefined is if there was a division by zero involved, but there is no division in this function. Therefore, the function f(x) is defined for all real numbers, including the options provided in the question.
None of the given options a) -2, b) 1, c) 0, d) 2 would make the function undefined. To conclude, f(x) is not undefined for any of the given values of x.