This math topic explores the concept of function domains, particularly focusing on functions that are structured as a linear fraction over the square root of a quadratic expression. The problems specifically deal with scenarios where the quadratic has complex roots, requiring students to determine the sets that correctly describe these functions' domains. Each question presents a different function, followed by multiple-choice options for students to select the correct domain representation. The skill being practiced involves understanding and identifying the conditions under which the functions' denominators are valid (non-zero and real).

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Function Domain - Fraction Linear over Root of Quadratic (Complex Roots) to Domain Definition

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What set describes the domain of this function?

f(x)=1x54x26x+18f(x) = \frac{1x-5}{\sqrt{4x^2-6x+18}}

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