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Consider the functions f, g given by f(x) = x - 6√, g(t) = 1/t³. (a) Find a formula for (f°g)(t). (b) Identify the practical domain of the composite function f°g.

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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.

User William Gunn
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