https://www.khanacademy.org/math/algebra-home/alg-functions/alg-combining-functions/v/sum-of-functions 2021-06-30T17:32:36Z Adding functions Given that f(x)=9-x^2 and g(x)=5x^2+2x+1, Sal finds (f+g)(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/vQo4H2MOShkJUwO2-h3Bj6ZvskipyaGS2sDl8f9RQSlUzaUiSg1HAaJGpn2r5qK_MFGruIxMkek26UyuWUfDQJXXDQ Adding functions Given that f(x)=9-x^2 and g(x)=5x^2+2x+1, Sal finds (f+g)(x). https://cdn.kastatic.org/ka-youtube-converted/n34dqyVCXs4.mp4/n34dqyVCXs4.mp4 153 Algebra of real functions https://www.khanacademy.org/math/algebra-home/alg-functions/alg-combining-functions/v/difference-of-functions 2021-06-30T17:32:38Z Subtracting functions Given that f(x)=2x√5-4 and g(x)=x^2+2x√5-1, Sal finds (g-f)(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/xl5HyNwZdnhKN5mhN2CIDDn3bMEV0T0scv9BRIbN5KBHYDmda4ERpzjR4OitpkO96VWeTcymCUeXgjT5RZ8XV2XG Subtracting functions Given that f(x)=2x√5-4 and g(x)=x^2+2x√5-1, Sal finds (g-f)(x). https://cdn.kastatic.org/ka-youtube-converted/6arI8XhLZ9o.mp4/6arI8XhLZ9o.mp4 136 Algebra of real functions https://www.khanacademy.org/math/algebra-home/alg-functions/alg-combining-functions/a/adding-and-subtracting-functions 2024-11-11T02:56:25.272408758Z Adding and subtracting functions See how we can add or subtract two functions to create a new function. article https://www.khanacademy.org/math/algebra-home/alg-functions/alg-combining-functions/v/product-of-functions 2021-06-30T17:32:39Z Multiplying functions Sal solves the following problem: given that f(x)=7x-5 and g(x)=x^3+4x, find (f*g)(x). He explains that generally, (f*g)(x)=f(x)*g(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/xKaLOaIfWxXnd1Z2TGBedcxXMuYJlrjbh1O9Dq_DS0VwjrP6X0C8UfVOk-4EUlaP0bQlKB5cRsP4QgPNUCKDNhP7 Multiplying functions Sal solves the following problem: given that f(x)=7x-5 and g(x)=x^3+4x, find (f*g)(x). He explains that generally, (f*g)(x)=f(x)*g(x). https://cdn.kastatic.org/ka-youtube-converted/JKvmAexeMgY.mp4/JKvmAexeMgY.mp4 180 Algebra of real functions https://www.khanacademy.org/math/algebra-home/alg-functions/alg-combining-functions/v/quotient-of-functions 2021-06-30T17:32:38Z Dividing functions Sal solves the following problem: given that f(x)=2x^2+15x-8 and g(x)=x^2+10x+16, find (f/g)(x). He explains that generally, (f/g)(x)=f(x)/g(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/LQhm8DE94i6gbuh6j4QkFQqISyUHwm__xaq5lZrD0uKKZ5HkryZQkfbRJHqZlHLF4gBgiupsp3c-1Dye81jxnt9- Dividing functions Sal solves the following problem: given that f(x)=2x^2+15x-8 and g(x)=x^2+10x+16, find (f/g)(x). He explains that generally, (f/g)(x)=f(x)/g(x). https://cdn.kastatic.org/ka-youtube-converted/u9v_bakOIcU.mp4/u9v_bakOIcU.mp4 378 Algebra of real functions https://www.khanacademy.org/math/algebra-home/alg-functions/alg-combining-functions/a/multiplying-and-dividing-functions 2024-12-05T04:53:33.617020624Z Multiplying and dividing functions See how we can multiply or divide two functions to create a new function. article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inputs-and-outputs-of-a-function/v/matching-function-input-to-output-with-graph 2021-05-05T14:53:16Z Worked example: matching an input to a function's output (graph) Sal finds the input value for which g(x)=-2 given the graph of g. video https://cdn.kastatic.org/googleusercontent/a8rSDx-YrrM8R6maqN-siR6uwCmMF1ycoEnZyTl5EdC4C6P79C1R4-lVsb_86V-c8R-1Kax9Kl2MlE6IK-cNMa6X Worked example: matching an input to a function's output (graph) Sal finds the input value for which g(x)=-2 given the graph of g. https://cdn.kastatic.org/ka-youtube-converted/0Rmmynff5Yc.mp4/0Rmmynff5Yc.mp4 67 Algebra of real functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inputs-and-outputs-of-a-function/e/match-inputs-to-outputs-from-a-graph 2026-04-07T23:17:37.123726494Z Function inputs & outputs: graph Find all the inputs that correspond to a given function output, using the function's graph. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inputs-and-outputs-of-a-function/v/different-inputs-giving-same-value-for-function 2021-05-05T14:53:18Z Worked example: two inputs with the same output (graph) Sal finds the input value other than -5 for which f(x)=f(-5), given the graph of f. video https://cdn.kastatic.org/googleusercontent/T9LS6JQUy_PBE6C53by--XCd1rUoo_Pz9PjxNKZ_e6ajw46YGN7ddiigWDIbk_cgr6OWA50xSkyGDr18pMQ_6BIZ Worked example: two inputs with the same output (graph) Sal finds the input value other than -5 for which f(x)=f(-5), given the graph of f. https://cdn.kastatic.org/ka-youtube-converted/qSktOkaW6EA.mp4/qSktOkaW6EA.mp4 108 Algebra of real functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inputs-and-outputs-of-a-function/v/finding-input-given-function-output-formula 2021-04-30T08:40:48Z Worked example: matching an input to a function's output (equation) Sal finds the input value for which f(t)=13, given that f(t)=-2t+5. video https://cdn.kastatic.org/googleusercontent/JlJoN6LFEZi-W_mdBLaiL4xij78NQhAsoFU5tLK680GG1i2oZEAiTv7j18Zivy8xlegoVTkMm5Y5Cz_CzxEyQl_N Worked example: matching an input to a function's output (equation) Sal finds the input value for which f(t)=13, given that f(t)=-2t+5. https://cdn.kastatic.org/ka-youtube-converted/tJBQZ3PUkPo.mp4/tJBQZ3PUkPo.mp4 100 Algebra of real functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inputs-and-outputs-of-a-function/e/functions_matching_inputs_outputs 2026-04-08T00:16:02.937952483Z Function inputs & outputs: equation Find all the inputs that correspond to a given function output, using the function's formula. Tomer Gal exercise