domain of f(x)= 7/(x-4)

{ "query": { "display": "domain $$f\\left(x\\right)=\\frac{7}{x-4}$$", "symbolab_question": "FUNCTION#domain f(x)=\\frac{7}{x-4}" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "domain", "default": "x<4\\lor x>4", "interval": "(-\\infty ,4)\\cup (4,\\infty )", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Domain of $$\\frac{7}{x-4}\\::{\\quad}x<4\\lor\\:x>4$$", "steps": [ { "type": "definition", "title": "Domain definition", "text": "The domain of a function is the set of input or argument values for which the function is real and defined" }, { "type": "interim", "title": "Find undefined (singularity) points:$${\\quad}x=4$$", "input": "\\frac{7}{x-4}", "steps": [ { "type": "step", "primary": "Take the denominator(s) of $$\\frac{7}{x-4}$$ and compare to zero" }, { "type": "interim", "title": "Solve $$x-4=0:{\\quad}x=4$$", "input": "x-4=0", "steps": [ { "type": "interim", "title": "Move $$4\\:$$to the right side", "input": "x-4=0", "result": "x=4", "steps": [ { "type": "step", "primary": "Add $$4$$ to both sides", "result": "x-4+4=0+4" }, { "type": "step", "primary": "Simplify", "result": "x=4" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve Title 1Eq" } }, { "type": "step", "primary": "The following points are undefined", "result": "x=4" } ], "meta": { "interimType": "Undefined Points 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7yzmeFdjgvhQTm0mwfI9L6t3Uj/l6EXvp8MVa8cTKNTj4KqpqHsTkSBgy/axoI6DanGB5QOm37WeTW5ROyPs6nciJn6ACoLXzcHc/ItMIlfiMQFCJrrV+N0fP+YW8YOr/XqsK+e1TiGj9RsLkU0NRYN34jETiAg5LEd3wdkcd1qfAvrFhiiwS4U0GvCPkqli3vUUGvlRczHDvLjdst2blpA==" } }, { "type": "step", "primary": "The function domain", "result": "x<4\\lor\\:x>4" } ], "meta": { "solvingClass": "Function Domain" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\frac{7}{x-4}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }