This math topic revolves around finding the domain of functions where the function's structure involves a linear fraction over the square root of a quadratic expression. Each problem presents a different function and asks to identify its domain represented on a number line. The primary skill focused here is handling expressions within square roots to determine the set of real numbers (x-values) that make the function’s denominator non-zero and the radicand non-negative. These problems help to reinforce understanding of function domains, particularly when working with square roots and quadratic expressions.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Function Domain - Fraction 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)=1x11x28x+9f(x) = \frac{1x-1}{\sqrt{-1x^2-8x+9}}

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