inverse of f(x)= 9/x

{ "query": { "display": "inverse $$f\\left(x\\right)=\\frac{9}{x}$$", "symbolab_question": "FUNCTION#inverse f(x)=\\frac{9}{x}" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "inverse", "default": "\\frac{9}{x}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Inverse of $$\\frac{9}{x}:{\\quad}\\frac{9}{x}$$", "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=\\frac{9}{x}" }, { "type": "interim", "title": "Replace $$x\\:$$with $$y$$", "input": "y=\\frac{9}{x}", "result": "x=\\frac{9}{y}", "steps": [ { "type": "step", "primary": "Replace $$x\\:$$with $$y$$", "secondary": [ "Replace $$y\\:$$with $$x$$" ], "result": "x=\\frac{9}{y}" } ], "meta": { "interimType": "Interchange Variables 2Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7vpqcDD/7yX5Tbd9fO9JFZdB593LpbfJhduIacCt/xPCD0yqNoTWLwGuqxO0C0cFVz5Lb2DzoR+2lK1ma7A4yFw7HH89RUTaeN3FUkEAdGm+LD3IXcw26W+fH/nWE+8Jg6uvWjigmDRR62v/uo5/c/6/iRbMPfLQeIqHWmDQDbe8=" } }, { "type": "interim", "title": "Solve for $$y,\\:x=\\frac{9}{y}$$", "input": "x=\\frac{9}{y}", "steps": [ { "type": "interim", "title": "Multiply both sides by $$y$$", "input": "x=\\frac{9}{y}", "result": "xy=9", "steps": [ { "type": "step", "primary": "Multiply both sides by $$y$$", "result": "xy=\\frac{9}{y}y" }, { "type": "step", "primary": "Simplify", "result": "xy=9" } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$x$$", "input": "xy=9", "result": "y=\\frac{9}{x}", "steps": [ { "type": "step", "primary": "Divide both sides by $$x$$", "result": "\\frac{xy}{x}=\\frac{9}{x}" }, { "type": "step", "primary": "Simplify", "result": "y=\\frac{9}{x}" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve For Title 2Eq" } }, { "type": "step", "result": "\\frac{9}{x}" } ], "meta": { "solvingClass": "Function Inverse" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\frac{9}{x}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }