Final answer:
The domain of the function F(x) = 7x^6 - 5x^4 + 3 is all real numbers because it is a polynomial function. Polynomial functions are defined for all real numbers, hence there are no restrictions on the domain.
Step-by-step explanation:
The domain of the function F(x) = 7x^6 - 5x^4 + 3 is the set of all real numbers, denoted by R. The reason is that the function involves only polynomial terms. In a polynomial, you can plug any real number for x, and it will result in a valid real-number output. Polynomial functions are defined for all real numbers, so the function doesn't have any restrictions on the domain.
For instance, the function won't produce undefined outputs for specific values of x as you might find with rational functions (fractions with x in the denominator) or radical functions (square roots, etc. with x in the radicand). Hence, in this case, the domain is all real numbers.
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