This math topic focuses on determining the domain of functions that involve the square root of a linear expression in the numerator and the square root of a quadratic expression in the denominator. Specifically, learners are tasked with mapping the real roots of these expressions on a number line. Each problem presents a different function, and students must choose the correct number line representation of the domain for each function.

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

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What number line shows the domain of this function?

f(x)=1x+51x26x5f(x) = \frac{\sqrt{1x+5}}{\sqrt{-1x^2-6x-5}}

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