The domain of the given inequality is y>1.
What is Inequality?
An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Here, given inequality:
y < [tex]\sqrt{x+3}+1[/tex]
Related equation:
y = [tex]\sqrt{x+3}+1[/tex]
The equation defined as,
x+3 > 0
x > -3
In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set. Thus, -3 is not included in the domain.
So, the domain of the given inequality is x>-3.
We know that,
[tex]\sqrt{x+3} \geq 0[/tex]
adding 1 on both sides, we get
[tex]\sqrt{x+3} + 1 \geq 1[/tex]
y ≥ 1
The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.
Thus, the domain of the given inequality is y>1.
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