inverse of x^3-11

{ "query": { "display": "inverse $$x^{3}-11$$", "symbolab_question": "FUNCTION#inverse x^{3}-11" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "inverse", "default": "\\sqrt[3]{x+11}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Inverse of $$x^{3}-11:{\\quad}\\sqrt[3]{x+11}$$", "steps": [ { "type": "definition", "title": "Function Inverse definition", "text": "A function g is the inverse of function f if for $$y=f\\left(x\\right),\\:\\:x=g\\left(y\\right)\\:$$" }, { "type": "step", "result": "y=x^{3}-11" }, { "type": "interim", "title": "Replace $$x\\:$$with $$y$$", "input": "y=x^{3}-11", "result": "x=y^{3}-11", "steps": [ { "type": "step", "primary": "Replace $$x\\:$$with $$y$$", "secondary": [ "Replace $$y\\:$$with $$x$$" ], "result": "x=y^{3}-11" } ], "meta": { "interimType": "Interchange Variables 2Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7vpqcDD/7yX5Tbd9fO9JFZe/OFW52n7DbvLnf+N0dLj8Idcllawnq1qNE+cowJkrTBottbu2aui7TA4izyM3ataN6Hv6MoTMtvtU0IQwXdn8cTGEY1u4y556Dta6zxSzhqWBEX8RwxAYJdvRdiwwWjubKioDhM4ng+kzyUOW2SCU=" } }, { "type": "interim", "title": "Solve for $$y,\\:x=y^{3}-11$$", "input": "x=y^{3}-11", "steps": [ { "type": "step", "primary": "Switch sides", "result": "y^{3}-11=x" }, { "type": "interim", "title": "Move $$11\\:$$to the right side", "input": "y^{3}-11=x", "result": "y^{3}=x+11", "steps": [ { "type": "step", "primary": "Add $$11$$ to both sides", "result": "y^{3}-11+11=x+11" }, { "type": "step", "primary": "Simplify", "result": "y^{3}=x+11" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } }, { "type": "step", "primary": "For $$x^n=f\\left(a\\right)$$, n is odd, the solution is $$x=\\sqrt[n]{f\\left(a\\right)}$$" }, { "type": "step", "result": "y=\\sqrt[3]{x+11}" } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve For Title 2Eq" } }, { "type": "step", "result": "\\sqrt[3]{x+11}" } ], "meta": { "solvingClass": "Function Inverse" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "x^{3}-11" }, "showViewLarger": true } }, "meta": { "showVerify": true } }