How to Find the Inverse of a Transformed Square Root Function (Step-by-Step)

TL;DW: Mastering inverse functions is all about algebra and visualization! In this part, we dive into finding the inverse of the transformed square root function f(x) = sqrt(x - 3) + 1. We start by graphing the function and seeing that our domain is [3, ∞) to ensure our function is defined within the real number system. By sketching the graph—shifting the parent function sqrt(x) right by 3 and up by 1—we confirm it is one-to-one, meaning an inverse exists! Key Steps in this Short: Isolate the radical by subtracting 1 from both sides. Square both sides to eliminate the square root. Solve for x to find the inverse: f^-1(y) = (y - 1)^2 + 3. Stay tuned for the next clip where we swap the variables and graph the result! #Algebra #InverseFunctions #Mathematics #PreCalculus #MathHelp #StepByStepMath #CalculusPrep #StudyTips #STEM #MathShorts Find the Inverse Function of a Transformed Square Root Function 📖 No-Nonsense Algebra: https://amzn.to/4hV5c3j. Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on LinkedIn:   / bill-kinney-a1246610   🔴 Follow me on Twitter:   / billkinneymath   🔴 Follow me on Instagram:   / billkinneymath   🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ 🔴 Desiring God website: https://www.desiringgod.org/ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.