Final answer:
The composite function (f°g)(t) is (1/t³) - √6 and its domain is all real numbers except t = 0.
Step-by-step explanation:
To find the composite function (f°g)(t), you replace every instance of 'x' in f(x) with g(t). In this case, f(x) = x - √6 and g(t) = 1/t³. Substituting, the composite function becomes:
(f°g)(t) = f(g(t)) = f(1/t³) = (1/t³) - √6.
The practical domain of (f°g)(t) is the set of all t values that do not make the denominator zero or the expression undefined. Since t cannot be zero because of the denominator 1/t³, the domain is all real numbers except t = 0.