Mathematics for Data Science 1 - W5_L2: One-to-one function examples, cubic cases & theorems

Welcome to Week 5 Lecture 2 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 lecture explores the concept of one-to-one functions through concrete examples and theorems. We examine functions like f(x) = |x| (modulus of x) and f(x) = x to check whether they are one-to-one using vertical and horizontal line tests. We also discuss cubic functions like f(x) = x_ and how to visually determine their one-to-one nature. Finally, we introduce the class of increasing and decreasing functions and prove that if f is an increasing or decreasing function, then f is necessarily one-to-one. 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 #onetoonefunction #injectivefunction #function #mathematics #calculus #horizontallinetest #verticallinetest #modulusfunction #cubicfunction #increasingfunction #decreasingfunction #functionproperties #datasciencemath #iitmadras #onlinestudy