This math topic focuses on determining the function domain involving fractions with square roots, where the numerator is a linear equation and the denominator contains quadratic expressions with complex roots. The problems require mapping these domains accurately onto a number line. Each question presents a different function expression and asks to identify the correct domain representation among multiple choices. This practice is part of a broader unit dealing with functions' domain and range solving skills, enhancing understanding of how function inputs are constrained by mathematical expressions.

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

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What number line shows the domain of this function?

f(x)=1x+34x2+6x17f(x) = \frac{\sqrt{1x+3}}{\sqrt{-4x^2+6x-17}}

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