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Some items also require graphing each function together with its inverse to confirm the reflection relationship across y = 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do you determine whether two functions are inverses?","Question",{"text":63,"@type":64},"By checking whether their compositions return the input, typically f(g(x)) = x and g(f(x)) = x, for the relevant domain.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What steps are used to find the inverse of a function?",{"text":68,"@type":64},"Replace f(x) with y, swap x and y, and solve the resulting equation for y to obtain f⁻¹(x).",{"name":70,"@type":61,"acceptedAnswer":71},"Why graph the function and its inverse together?",{"text":72,"@type":64},"To verify that the inverse is the mirror image of the original function across the line y = 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Inverses Date  Period   \nState if the given functions are inverses.  \n1) g(x) = 4 − ~~ ~~32xf (x) = 12x + ~~ ~~32  \n3) f (n) = −164+~~ ~~ng(n) = 4n + 16  \n5) f (n) = −(n + 1) 3 g(n) = 3 + n 3  \n7) f (x) = −x~~ ~~2 + 2 h(x) = − ~~ ~~x~~ ~~~~ ~~3  \n2) g(n) = −12~~ ~~2nf (n) = −5~~ ~~+5~~ ~~6n  \n4) f (x) = − ~~ ~~47x − ~~ ~~167 g( x) = ~~ ~~32x − ~~ ~~32  \n6) f (n) = 2(n − 2) 3 3  \ng(n) = ~~ ~~4~~ ~~+~~ ~~2~~ ~~4n  \n8) g(x) = − ~~ ~~2x − 1 f (x) = − ~~ ~~x~~ ~~~~ ~~1  \nFind the inverse of each function.  \n9) h(x) = x − 3 10) g(x) = ~~ ~~1x − 2  \n11) h(x) = 2x3 + 3 12) g(x) = −4x + 1  \n7x + 18 14) f (x) = x + 3  \n13) g(x) =  2   \n15) f (x) = −x + 3 16) f (x) = 4x  \nFind the inverse of each function. Then graph the function and its inverse.  \n17) f (x) = −1 − ~~ ~~15x  \n\n| |  |  |  |  |  |  | y |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 5 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 4 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 3 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 2 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 1 |  |  |  |  |  |  |  |\n| − | 6 − | 5 − | 4 − | 3 − | 2 − | 1 |  | 1 2 | 3 | 4 | 5 | 6 | x |\n|  |  |  |  |  |  | −1 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −2 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −3 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −4 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −5 |  |  |  |  |  |  |  |\n| −6\u003Cbr>|  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n6  \n19) f (x) = −2x3 + 1  \n\n| |  |  |  |  |  |  | y |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 5 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 4 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 3 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 2 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 1 |  |  |  |  |  |  |  |\n| − | 6 − | 5 − | 4 − | 3 − | 2 − | 1 |  | 1 2 | 3 | 4 | 5 | 6 | x |\n|  |  |  |  |  |  | −1 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −2 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −3 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −4 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −5 |  |  |  |  |  |  |  |\n| −6\u003Cbr>|  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n6  \n18) g(x) = ~~ ~~x~~ ~~~~ ~~1  \n\n| |  |  |  |  |  |  | y |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 5 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 4 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 3 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 2 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 1 |  |  |  |  |  |  |  |\n| − | 6 − | 5 − | 4 − | 3 − | 2 − | 1 |  | 1 2 | 3 | 4 | 5 | 6 | x |\n|  |  |  |  |  |  | −1 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −2 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −3 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −4 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −5 |  |  |  |  |  |  |  |\n| −6\u003Cbr>|  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n6  \n20) g(x) = −x~~ ~~5  \n\n| |  |  |  |  |  |  | y |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 5 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 4 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 3 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 2 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | 1 |  |  |  |  |  |  |  |\n| − | 6 − | 5 − | 4 − | 3 − | 2 − | 1 |  | 1 2 | 3 | 4 | 5 | 6 | x |\n|  |  |  |  |  |  | −1 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −2 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −3 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −4 |  |  |  |  |  |  |  |\n|  |  |  |  |  |  | −5 |  |  |  |  |  |  |  |\n| −6\u003Cbr>|  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n6  \nKuta Software-Infinite Algebra 2 Name   \nFunction Inverses Date  Period   \nState if the gi","cbCaitRIzcxFiqYn","https://ap.wps.com/l/cbCaitRIzcxFiqYn","pdf",42325,"English","# State if the given functions are inverses\n## Check inverse pairs\n# Find the inverse of each function\n## Linear and nonlinear examples\n# Find the inverse and graph both","[{\"question\":\"How do you determine whether two functions are inverses?\",\"answer\":\"By checking whether their compositions return the input, typically f(g(x)) = x and g(f(x)) = x, for the relevant domain.\"},{\"question\":\"What steps are used to find the inverse of a function?\",\"answer\":\"Replace f(x) with y, swap x and y, and solve the resulting equation for y to obtain f⁻¹(x).\"},{\"question\":\"Why graph the function and its inverse together?\",\"answer\":\"To verify that the inverse is the mirror image of the original function across the line y = x.\"}]","Function Inverses - Infinite Algebra 2 - Worksheet | PDF",1791426031]