https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/v/function-composition 2023-04-03T21:40:12.365083232Z Intro to composing functions This video is about composing functions, which is the process of building up a function by composing it from other functions. It explains how to evaluate the composition of functions step by step, using examples with three different function definitions: f (x), g(t), and h(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/oFlXj7HzyrhyxvG_Yu6VUREb1D8SFPYfTXdYMjNZ8IRCsqcb7iQ6JMTPIaErn9TpUBuxsSjuXVfmv2B0l23ffSgYbQ Intro to composing functions This video is about composing functions, which is the process of building up a function by composing it from other functions. It explains how to evaluate the composition of functions step by step, using examples with three different function definitions: f (x), g(t), and h(x). https://cdn.kastatic.org/ka-youtube-converted/wUNWjd4bMmw.mp4/wUNWjd4bMmw.mp4 375 Composition of functions and invertible function https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/v/evaluating-composite-functions 2022-10-07T00:22:18.752150461Z Evaluating composite functions Sal evaluates (h⚬g)(-6) for g(x)=x²+5x-3 and h(y)=3(y-1)²-5. video https://cdn.kastatic.org/ka_thumbnails_cache/e6f1b3f6-3917-42a6-8cc0-695655b73fd6_1280_720_base.png Evaluating composite functions Sal evaluates (h⚬g)(-6) for g(x)=x²+5x-3 and h(y)=3(y-1)²-5. https://cdn.kastatic.org/ka-youtube-converted/lxtlwnCV-HM.mp4/lxtlwnCV-HM.mp4 250 Composition of functions and invertible function https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/v/new-function-from-composition 2023-07-18T22:48:45.033562364Z Finding composite functions Through a worked example involving f(x)=√(x²-1) and g(x)=x/(1+x), learn about function composition: the process of combining two functions to create a new function. This involves replacing the input of one function with the output of another function. Also note that the composition of two functions is typically not the same as their composition in the reverse order. Sal Khan video https://cdn.kastatic.org/googleusercontent/5uNkRakTQjdWVltWmPnETUCEp1SkdEtER8bW9NjVyBzMQ31W2yM4ZMutYYnxEEsIpytv1kXUxXoCMz4zCeF7CeI1UA Finding composite functions Through a worked example involving f(x)=√(x²-1) and g(x)=x/(1+x), learn about function composition: the process of combining two functions to create a new function. This involves replacing the input of one function with the output of another function. Also note that the composition of two functions is typically not the same as their composition in the reverse order. https://cdn.kastatic.org/ka-youtube-converted/_b-2rZpX5z4.mp4/_b-2rZpX5z4.mp4 177 Composition of functions and invertible function https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/e/evaluate-composite-functions-from-formulas 2025-03-03T19:47:54.930712342Z Evaluate composite functions Given the formulas of two functions, evaluate the composition of the two functions at a given input. Stacy Beaudoin exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/e/compose-functions 2025-05-05T08:14:25.350149109Z Find composite functions Given the formulas of two functions, find the formula of their composition. Charlotte Auen exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:invertible/v/determining-if-a-function-is-invertible 2023-07-18T22:48:45.033562364Z Determining if a function is invertible Learn how to build a mapping diagram for a finite function, and how to use this diagram to determine if the function is invertible. An invertible function has a one-to-one mapping between its domain and range. Functions that map multiple domain elements to the same range element are not invertible. video https://cdn.kastatic.org/ka_thumbnails_cache/f2547404-81e7-482d-b049-13297674c2ac_1280_720_base.png Determining if a function is invertible Learn how to build a mapping diagram for a finite function, and how to use this diagram to determine if the function is invertible. An invertible function has a one-to-one mapping between its domain and range. Functions that map multiple domain elements to the same range element are not invertible. https://cdn.kastatic.org/ka-youtube-converted/dqCTAHHza10.mp4/dqCTAHHza10.mp4 244 Composition of functions and invertible function https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:invertible/e/inverse-domain-range 2026-04-08T00:36:09.500768563Z Determine if a function is invertible Given the table of values of a function, determine whether it is invertible or not. Stacy Beaudoin exercise