Mathematics for Data Science 1 - W8_T6: Domain of composite functions with examples

Welcome to Week 8 Tutorial 6 of the course "Mathematics for Data Science I" by Profs. Neelesh Upadhye, Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMA1001.html Video Overview This tutorial explores how to determine the domain of a composite function, f(g(x)). Using examples like f(x) = (x_ - 8x + 15) / (x + 3) and g(x) = √(x_ - 4), we walk through the process step by step. First, we identify the domain of g(x), then analyze how the range of g(x) interacts with the domain of f(x). We also consider special cases where values must be excluded to ensure the composite function is valid. A second example further illustrates these ideas and strengthens understanding of domain analysis in composite functions. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #compositefunction #functiondomain #domainoffunction #functioncomposition #mathematics #calculus #functionanalysis #domainandrange #math #precalculus #datasciencemath #iitmadras #onlinestudy