The domain the function is [tex]x\geq 7[/tex]
In interval notation: [7, ∞)
The range of the function is in the interval (1, ∞).
Given function:
[tex]y=\sqrt{x-7} +1[/tex]
Find the domain of the function:
In this case you do not want a negative argument for the square root (you cannot find the solution of a negative square root, at least as a real number).
What you do it is to "impose" that the argument is always positive or zero (you know the square root of a positive number or zero).
So you set the argument bigger or equal to zero and solve for x to find the ALLOWED values of your variable:
[tex]x-7\geq 0\\x\geq 7[/tex]
Therefore, the domain the function is [tex]x\geq 7[/tex]
Find the range of the function:
Range of the function is the set of all values of y when we substitute the values of x.
For, x = 7
[tex]y=\sqrt{7-7}+1\\y=1[/tex]
So, the value of y in the interval (1, ∞).
Therefore, the range of the function is in the interval (1, ∞).
For more information:
https://brainly.com/question/19560386
