Respuesta :

Answer:option 3, Y is greater than or = to -1

Step-by-step explanation:

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The range of [tex]y=\sqrt{x-5} -1[/tex]   is [tex][-1,\infty)[/tex].

Given,

[tex]y=\sqrt{x-5} -1[/tex].

We have to find the range of the expression.

Set the radicand in [tex]\sqrt{x-5}[/tex]  greater than or equal to 0  to find where the expression is defined.

[tex]\sqrt{x-5} \geq 0[/tex]

[tex]x-5\geq 0[/tex]  

Add 5 to both sides of the inequality, we get

[tex]x\geq 5[/tex]

The domain is all values of [tex]x[/tex] that make the expression defined.

Interval Notation:

[tex][5,\infty )[/tex]

Set-Builder Notation:

[tex][x|x\geq 5][/tex]

The range of an even indexed radical starts at its starting point  ( 5 , − 1 )  and extends to infinity.

Interval notation:

[tex][-1,\infty)[/tex]

Hence the range of above function is [tex][-1,\infty)[/tex].

For more details on range follow the link:

https://brainly.com/question/8041076