Question

Domain and range of the inequality y<√x+3 +1

Answer 1

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 < $\sqrt{x+3}+1$

Related equation:

             y = $\sqrt{x+3}+1$

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,

    $\sqrt{x+3} \geq 0$

adding 1 on both sides, we get

  $\sqrt{x+3} + 1 \geq 1$

      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.

Learn more about Inequality from:

brainly.com/question/20383699

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