inverse of x-4

{ "query": { "display": "inverse $$x-4$$", "symbolab_question": "FUNCTION#inverse x-4" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "inverse", "default": "x+4", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Inverse of $$x-4:{\\quad}x+4$$", "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=x-4" }, { "type": "interim", "title": "Replace $$x\\:$$with $$y$$", "input": "y=x-4", "result": "x=y-4", "steps": [ { "type": "step", "primary": "Replace $$x\\:$$with $$y$$", "secondary": [ "Replace $$y\\:$$with $$x$$" ], "result": "x=y-4" } ], "meta": { "interimType": "Interchange Variables 2Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7vpqcDD/7yX5Tbd9fO9JFZRG81QzFGB0OGkNLsNozHEH6Zij41f8AqYfKZ45rc2etAjz6GQvIClnX85LTbcJNv9bA+zX4bD3u3gx65o2NJhNwxulPA7WpzPVXeG0Na/5/8wLli62Dp9y4S6imP//7Jw==" } }, { "type": "interim", "title": "Solve for $$y,\\:x=y-4$$", "input": "x=y-4", "steps": [ { "type": "step", "primary": "Switch sides", "result": "y-4=x" }, { "type": "interim", "title": "Move $$4\\:$$to the right side", "input": "y-4=x", "result": "y=x+4", "steps": [ { "type": "step", "primary": "Add $$4$$ to both sides", "result": "y-4+4=x+4" }, { "type": "step", "primary": "Simplify", "result": "y=x+4" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve For Title 2Eq" } }, { "type": "step", "result": "x+4" } ], "meta": { "solvingClass": "Function Inverse" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "x-4" }, "showViewLarger": true } }, "meta": { "showVerify": true } }