range of f(x)=sqrt(x-2)+1

{ "query": { "display": "range $$f\\left(x\\right)=\\sqrt{x-2}+1$$", "symbolab_question": "FUNCTION#range f(x)=\\sqrt{x-2}+1" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Functions", "subTopic": "range", "default": "f(x)\\ge 1", "interval": "[1,\\infty )", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Range of $$\\sqrt{x-2}+1:{\\quad}f\\left(x\\right)\\ge\\:1$$", "steps": [ { "type": "definition", "title": "Function range definition", "text": "The set of values of the dependent variable for which a function is defined" }, { "type": "step", "primary": "The range of an radical function of the form $$c\\sqrt{ax+b}+k\\:$$is $$f\\left(x\\right)\\ge\\:k$$", "secondary": [ "$$k=1$$" ], "result": "f\\left(x\\right)\\ge\\:1" } ], "meta": { "solvingClass": "Function Range" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\sqrt{x-2}+1" }, "showViewLarger": true } }, "meta": { "showVerify": true } }