Final answer:
The domain of a function is a set of all possible input values which will produce real output values. In the given function, we need to exclude values of x which will make the denominator to zero as it is undefined to divide by zero. However, due to an unclear fraction, we need more information to provide a precise domain.
Step-by-step explanation:
The function provided in the question is f(x) = 5x³ - 3/x² + 3x - 10. The domain of a function is the set of all possible input values (x-values) which will give real output values (y-values). The only restrictions for the domain would be values for which the function is undefined. Generally, in the fraction the denominator cannot be zero, so we should solve the equation x² + 3x - 10 = 0 to exclude the values of x from the domain that will make the function undefined. However the question does not specify the equation clearly whether the denominator is 'x² + 3x' or 'x² + 3x - 10' only then we can solve the equation. Given the uncertainty, we need a clarification to provide an accurate answer for the domain.
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