The domain for g (x) - f (x) = x² - x - 12 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
We are given the two functions as:
f (x) = x - 4
g (x) = x² - 16
Now, first, we need to subtract f (x) from g (x).
So, we get that:
g (x) - f (x) = x² - 16 - (x - 4)
g (x) - f (x) = x² - 16 - x + 4
g (x) - f (x) = x² - x - 12
Now, the domain of the function will be all real numbers as it will be defined for all the real numbers.
Therefore, we get that the domain for g (x) - f (x) = x² - x - 12 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
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