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

This math topic focuses on determining the domain of functions that are fractions with an integer numerator and a square root of a quadratic expression in the denominator. Each problem involves analyzing the quadratic under the root to ensure the expression inside remains non-negative (since a square root must yield a real number). The problems require students to set up inequalities based on the quadratic discriminant or properties ensuring the radicand is non-negative and solve these inequalities to specify the variable's domain where the function is defined. The answers are provided in set notation, expressing conditions on the variable.