Math  /  Algebra

QuestionFind (st)(x)(s \cdot t)(x) for s(x)=x3x236s(x) = \frac{x-3}{x^{2}-36} and t(x)=x63xt(x) = \frac{x-6}{3-x}. State the domain in interval notation.

Studdy Solution
The function is undefined when x=6x = -6. Therefore, the domain of the function is all real numbers except 6-6. In interval notation, this is written as (,6)(6,)(-\infty, -6) \cup (-6, \infty).
The product of the functions s(x)=xx236s(x) = \frac{x-}{x^{2}-36} and t(x)=x6xt(x) = \frac{x-6}{-x} is (st)(x)=x+6(s \cdot t)(x) = \frac{-}{x+6}, and the domain of this new function is (,6)(6,)(-\infty, -6) \cup (-6, \infty).

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