{
"query": {
"display": "range $$f\\left(x\\right)=2\\sqrt{x+3}-1$$",
"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": "Range of $$2\\sqrt{x+3}-1:{\\quad}f\\left(x\\right)\\ge\\:-1$$",
"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": "2\\sqrt{x+3}-1"
},
"showViewLarger": true
}
},
"meta": {
"showVerify": true
}
}
Solution
range
Solution
+1
Interval Notation
Solution steps
The range of an radical function of the form is
Graph
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Frequently Asked Questions (FAQ)
What is the range of f(x)=2sqrt(x+3)-1 ?
The range of f(x)=2sqrt(x+3)-1 is f(x)>=-1