inverse of f(x)=((x-4))/3

{ "query": { "display": "inverse $$f\\left(x\\right)=\\frac{\\left(x-4\\right)}{3}$$", "symbolab_question": "FUNCTION#inverse f(x)=\\frac{(x-4)}{3}" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "inverse", "default": "3x+4", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Inverse of $$\\frac{x-4}{3}:{\\quad}3x+4$$", "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{x-4}{3}" }, { "type": "interim", "title": "Replace $$x\\:$$with $$y$$", "input": "y=\\frac{x-4}{3}", "result": "x=\\frac{y-4}{3}", "steps": [ { "type": "step", "primary": "Replace $$x\\:$$with $$y$$", "secondary": [ "Replace $$y\\:$$with $$x$$" ], "result": "x=\\frac{y-4}{3}" } ], "meta": { "interimType": "Interchange Variables 2Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7vpqcDD/7yX5Tbd9fO9JFZWtm4E5dkich/zhBSBfcTxa5kHDh/wfDJsn28Gt2EY20uT7NM3IgGSg7KvASoIT1+CGdMQWj7euUj19HIJMZ9JN6PZq4pYr+MqS+U8UJjX531Kuuv9CNQvrdvkZ5dLi5r5KKTpUQqDZ50xP6ow8quMY=" } }, { "type": "interim", "title": "Solve for $$y,\\:x=\\frac{y-4}{3}$$", "input": "x=\\frac{y-4}{3}", "steps": [ { "type": "step", "primary": "Switch sides", "result": "\\frac{y-4}{3}=x" }, { "type": "interim", "title": "Multiply both sides by $$3$$", "input": "\\frac{y-4}{3}=x", "result": "y-4=3x", "steps": [ { "type": "step", "primary": "Multiply both sides by $$3$$", "result": "\\frac{3\\left(y-4\\right)}{3}=3x" }, { "type": "step", "primary": "Simplify", "result": "y-4=3x" } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Move $$4\\:$$to the right side", "input": "y-4=3x", "result": "y=3x+4", "steps": [ { "type": "step", "primary": "Add $$4$$ to both sides", "result": "y-4+4=3x+4" }, { "type": "step", "primary": "Simplify", "result": "y=3x+4" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7T1zPNCgUauMS+3DEaj/fYRyOUtErWNRXbTqqjj69E3uOYRm6x5AiUCacb1IpRyiBRKvwpCsMm/dIDWKdnSUJtEju2mcSNhRfU7C4yjhCb7wKMGIUrN5C+fJvZZbizphFZstIgwW/a/X8v6hAcC4x0gL0wYz8T26ax1m7Hwnc9y7oR99OrdeZNbC3FdLyvzS75SYwRGnNsdKdLmRVVroKc8RQ+TsbddHVBEbjW9NqnYb8kb6uJMr/5RE46n+o9NkrDAoC7tne039GAs+OXPJHDyLk6g02mupBXZSBBQYRKoWW+OGpCzlckmQe/YZBQTqCVysA6xE5+JWA/7C1bKHRp+2G/AoShHeSwc0dsKStvqRzAMh/Fuv8+ra9aOxcF2mY/4Zzu40OfmsUyIPK/r2eIpL2clglKffbeQE6AssklIcOdeXnNKQQopErd/enLG0af1iKGIZH+SGJ+Pb2nr6myg==" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve For Title 2Eq" } }, { "type": "step", "result": "3x+4" } ], "meta": { "solvingClass": "Function Inverse" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\frac{x-4}{3}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }