If the domain of each of the functions f (x) and g (x) is all real numbers, will the domain of (f/g) (x) also be all real numbers

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Mathematics

Yadira

6 January, 15:08

If the domain of each of the functions f (x) and g (x) is all real numbers, will the domain of (f/g) (x) also be all real numbers

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Cale Douglas · Answer 1

Yes, the biggest giveaway to understanding this problem is what can does a fraction have restrictions on. Since x cannot be 0, in the example: 1/x, then, the domain is all real numbers, except for 0.

So, to tackle this problem, let's consider the restrictions of g (x). Now, we know that g (x) cannot be zero, since that will render the fraction indeterminate. So, we know g (x) ≠ 0. But that's not the same as g (0).

If there are no restrictions on g (x), then the function will be continuous for all x.