domain of f(x)=\sqrt[3]{|x|-1/x}

{ "query": { "display": "domain $$f\\left(x\\right)=\\sqrt[3]{\\left|x\\right|-\\frac{1}{x}}$$", "symbolab_question": "FUNCTION#domain f(x)=\\sqrt[3]{\\left|x\\right|-\\frac{1}{x}}" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "domain", "default": "x<0\\lor x>0", "interval": "(-\\infty ,0)\\cup (0,\\infty )", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Domain of $$\\sqrt[3]{\\left|x\\right|-\\frac{1}{x}}\\::{\\quad}x<0\\lor\\:x>0$$", "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:$${\\quad}x=0$$", "input": "\\sqrt[3]{\\left|x\\right|-\\frac{1}{x}}", "steps": [ { "type": "step", "primary": "Take the denominator(s) of $$\\sqrt[3]{\\left|x\\right|-\\frac{1}{x}}$$ and compare to zero" }, { "type": "step", "result": "x=0" }, { "type": "step", "primary": "The following points are undefined", "result": "x=0" } ], "meta": { "interimType": "Undefined Points 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7yzmeFdjgvhQTm0mwfI9L6nmg7Mhjifp1dOEFBP30e1DVb9mhQ+Ih00TcsPAUqYigBsV3dxG6v0a6NSuoa/K2ghbKmzZVnNMO2vvDVwZiPhEJq0QcjuN2KUmUwyXe4BaDQnlefM1LTzGHqEjfxtQyoGRLd2VwIqlBNByF6663syS79IfwZes35cnTMonSYr4arKJsMOQibrCySif/MgmEj++h9PsrnIlVhvpJW9KAzdE=" } }, { "type": "step", "primary": "The function domain", "result": "x<0\\lor\\:x>0" } ], "meta": { "solvingClass": "Function Domain" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\sqrt[3]{\\left|x\\right|-\\frac{1}{x}}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }