This math topic focuses on determining the function domains where functions involve the ratio of the square root of a linear expression to the square root of a quadratic expression with real roots. Students are asked to identify the correct set that describes the domain of such functions in multiple-choice format. This topic aims to strengthen skills in analyzing the behavior of function denominators, particularly concerning the conditions that allow for real and defined outputs, such as ensuring non-negative values under the square roots and non-zero quadratic expressions. This is foundational in understanding function behavior in higher mathematics, particularly in algebra and calculus.

more

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


What set describes the domain of this function?

f(x)=1x+11x2+2x3f(x) = \frac{\sqrt{1x+1}}{\sqrt{1x^2+2x-3}}

?