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Domain of Composite Functions (Logarithmic ∘ Quadratic Examples)

This video explains how to determine the domain of composite functions when a logarithmic function is composed with a quadratic function. We examine both f(g(x)) and g(f(x)), showing how the logarithmic argument imposes a strict (greater than 0) condition and how the quadratic expression creates interval-based solutions for the domain. This topic appears frequently in first-year calculus exams, particularly in sections on functions, composition, and domain analysis. 📘 Topics covered: • Domain restrictions from logarithmic functions • Interval restrictions from quadratic expressions • Comparing f(g(x)) vs g(f(x)) • Solving inequalities to determine valid inputs • Worked examples step-by-step Suitable for undergraduate mathematics students revising composite functions and domain concepts.