Determine the domain of the function g(t)=√7−t−√4+t.

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BlackTom AI · Accepted Answer

To determine the domain of g(t) = sqrt(7 - t) - sqrt(4 + t), we must ensure the expressions under both square roots are nonnegative.
First, require 7 - t ≥ 0, which gives t ≤ 7. This restricts t to the left of or at 7.
Next, require 4 + t ≥ 0, which gives t ≥ -4. This restricts t to the right of or at -4.
The domain of the function is the intersection of these two conditions: t ≤ 7 and t ≥ -4, which yields -4 ≤ t ≤ 7.
If there were multiple-choice options, we would look for an option that corresponds to this interval. Since no options are provided in the prompt, the domain is the set of all t between -4 and 7 inclusive, i.e., [-4, 7].

MATH 2A LEC A: CALCULU... Quiz 1 (Multiple Choice)

Determine the domain of the function g(t)=√7−t−√4+t.

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