The domain of the function is [-5,0) and the range of the function y = startroot x 5 endroot is [0,∞)
Range of a function is the set of all the possible output values which are valid for that function.
The function given in the problem is,
[tex]y=\sqrt{x+5}[/tex]
This function is defined when the value of √(x+5) is greater than or equal to 0.
[tex]\sqrt{x+5}\ge0[/tex]
Solve it further,
[tex]\sqrt{x+5}\ge0\\(x+5)\ge0\\x\ge-5[/tex]
Thus, the domain of the equation is [-5,0). Now for the range,
[tex]x+5\ge0\\\sqrt{x+5}\ge0\\y\ge0[/tex]
Thus the range is [0,∞).
Hence, the domain of the function is [-5,0) and the range of the function y = startroot x 5 endroot is [0,∞)
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