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What are the domain and range of the inequality y < sqrt x+3+1

I don't get it I try to solve it but I just didn't get .

What are the domain and range of the inequality y < sqrt x+3+1 I don't get it I-example-1
User Eulenfuchswiesel
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1 Answer

14 votes
14 votes

Given:

The inequality is:


y<√(x+3)+1

To find:

The domain and range of the given inequality.

Solution:

We have,


y<√(x+3)+1

The related equation is:


y=√(x+3)+1

This equation is defined if:


x+3\geq 0


x\geq -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,


√(x+3)\geq 0


√(x+3)+1\geq 0+1


y\geq 1

The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.

So, the domain of the given inequality is y>1.

Therefore, the correct option is A.

User Berbatov
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