Set the radicand in <math><mstyle displaystyle="true"><msqrt><mi>x</mi><mo>+</mo><mn>1</mn></msqrt></mstyle></math> greater than or equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to find where the expression is defined.

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from both sides of the inequality.

The domain is all values of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> that make the expression defined.

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Interval Notation:

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Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> in the expression.

Simplify the result.

Simplify each term.

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

The radical expression end point is <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> .

Substitute the <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> value <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> into <math><mstyle displaystyle="true"><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>3</mn><mo>-</mo><msqrt><mi>x</mi><mo>+</mo><mn>1</mn></msqrt></mstyle></math> . In this case, the point is <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math> .

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> in the expression.

Simplify the result.

Simplify each term.

Add <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Any root of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Substitute the <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> value <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> into <math><mstyle displaystyle="true"><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>3</mn><mo>-</mo><msqrt><mi>x</mi><mo>+</mo><mn>1</mn></msqrt></mstyle></math> . In this case, the point is <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>)</mo></mrow></mstyle></math> .

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the expression.

Simplify the result.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>3</mn><mo>-</mo><msqrt><mn>2</mn></msqrt></mstyle></math> .

The square root can be graphed using the points around the vertex <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>1.59</mn><mo>)</mo></mrow></mstyle></math>

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Name | one billion eight hundred thirty-four million five hundred forty-one thousand eight hundred forty-nine |
---|

- 1834541849 has 4 divisors, whose sum is
**2096619264** - The reverse of 1834541849 is
**9481454381** - Previous prime number is
**7**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 47
- Digital Root 2

Name | four hundred nineteen million six hundred one thousand five hundred forty-two |
---|

- 419601542 has 4 divisors, whose sum is
**629402316** - The reverse of 419601542 is
**245106914** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 32
- Digital Root 5

Name | nine hundred ninety-eight million eight hundred four thousand five |
---|

- 998804005 has 8 divisors, whose sum is
**1198734624** - The reverse of 998804005 is
**500408899** - Previous prime number is
**14851**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 43
- Digital Root 7