inverse of f(x)=(6x+4)/(x-1)

{ "query": { "display": "inverse $$f\\left(x\\right)=\\frac{6x+4}{x-1}$$", "symbolab_question": "FUNCTION#inverse f(x)=\\frac{6x+4}{x-1}" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "inverse", "default": "\\frac{4+x}{x-6}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Inverse of $$\\frac{6x+4}{x-1}:{\\quad}\\frac{4+x}{x-6}$$", "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{6x+4}{x-1}" }, { "type": "interim", "title": "Replace $$x\\:$$with $$y$$", "input": "y=\\frac{6x+4}{x-1}", "result": "x=\\frac{6y+4}{y-1}", "steps": [ { "type": "step", "primary": "Replace $$x\\:$$with $$y$$", "secondary": [ "Replace $$y\\:$$with $$x$$" ], "result": "x=\\frac{6y+4}{y-1}" } ], "meta": { "interimType": "Interchange Variables 2Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7vpqcDD/7yX5Tbd9fO9JFZflKb+oE8YY1V5eRRX8iWLZqBnuJ6LoqjdABV7VIPgGrGQmYVIcZpIrwEyqT9Afp8/wjxGUyXxWBxRqXMq0bSOpN5Aod6Hr1Lp2e/29KhSgUmjqleygtlSszoezKDjz2k7GJwpZAgCxm4WPlcU4xj5k=" } }, { "type": "interim", "title": "Solve for $$y,\\:x=\\frac{6y+4}{y-1}$$", "input": "x=\\frac{6y+4}{y-1}", "steps": [ { "type": "interim", "title": "Multiply both sides by $$y-1$$", "input": "x=\\frac{6y+4}{y-1}", "result": "x\\left(y-1\\right)=6y+4", "steps": [ { "type": "step", "primary": "Multiply both sides by $$y-1$$", "result": "x\\left(y-1\\right)=\\frac{6y+4}{y-1}\\left(y-1\\right)" }, { "type": "step", "primary": "Simplify", "result": "x\\left(y-1\\right)=6y+4" } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": 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"step", "primary": "Multiply: $$1\\cdot\\:x=x$$", "result": "=xy-x" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Expand Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7OFqCkI9WIzzlAz4kmV7GyAsBmUOGgB0VAXoAXik9qC9EoApuujwRq/Ms3wa4gNT89ZVSO0B13oSpK+zJfqv7kB7MWKURN+43KCOzRc+RXaGuSZBSS2yDJsYvLH1YSvDL" } }, { "type": "step", "result": "xy-x=6y+4" }, { "type": "interim", "title": "Move $$x\\:$$to the right side", "input": "xy-x=6y+4", "result": "xy=6y+4+x", "steps": [ { "type": "step", "primary": "Add $$x$$ to both sides", "result": "xy-x+x=6y+4+x" }, { "type": "step", "primary": "Simplify", "result": "xy=6y+4+x" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": 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"y\\left(x-6\\right)=4+x" }, { "type": "interim", "title": "Divide both sides by $$x-6$$", "input": "y\\left(x-6\\right)=4+x", "result": "y=\\frac{4+x}{x-6}", "steps": [ { "type": "step", "primary": "Divide both sides by $$x-6$$", "result": "\\frac{y\\left(x-6\\right)}{x-6}=\\frac{4}{x-6}+\\frac{x}{x-6}" }, { "type": "interim", "title": "Simplify", "input": "\\frac{y\\left(x-6\\right)}{x-6}=\\frac{4}{x-6}+\\frac{x}{x-6}", "result": "y=\\frac{4+x}{x-6}", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{y\\left(x-6\\right)}{x-6}:{\\quad}y$$", "input": "\\frac{y\\left(x-6\\right)}{x-6}", "steps": [ { "type": "step", "primary": "Cancel the common factor: $$x-6$$", "result": "=y" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": 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