{ "query": { "display": "rango $$f\\left(x\\right)=2\\sqrt{x+3}-1$$", "symbolab_question": "FUNCTION#range f(x)=2\\sqrt{x+3}-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": "Rango de $$2\\sqrt{x+3}-1:{\\quad}f\\left(x\\right)\\ge\\:-1$$", "steps": [ { "type": "definition", "title": "Definición de rango de función", "text": "El conjunto de valores de la variable dependiente para la que se define una función" }, { "type": "step", "primary": "El rango de una función con radicales de la forma $$c\\sqrt{ax+b}+k\\:$$es $$f\\left(x\\right)\\ge\\:k$$", "secondary": [ "$$k=-1$$" ], "result": "f\\left(x\\right)\\ge\\:-1" } ], "meta": { "solvingClass": "Function Range" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "2\\sqrt{x+3}-1" }, "showViewLarger": true } }, "meta": { "showVerify": true } }