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.

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

Interval Notation:

Set-Builder Notation:

Interval Notation:

Set-Builder Notation:

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.

Simplify each term.

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from <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"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

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

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

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> in the expression.

Simplify the result.

Simplify each term.

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>2</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"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

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

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> in the expression.

Simplify the result.

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><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>3</mn></mstyle></math> .

The square root can be graphed using the points around the vertex <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>0.17</mn><mo>)</mo></mrow></mstyle></math>

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Name | one billion two hundred seventy-seven million nine hundred thirty-nine thousand two hundred forty-two |
---|

- 1277939242 has 8 divisors, whose sum is
**1917078336** - The reverse of 1277939242 is
**2429397721** - Previous prime number is
**15643**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 46
- Digital Root 1

Name | one billion one hundred eight million one hundred seventy-one thousand five hundred nineteen |
---|

- 1108171519 has 16 divisors, whose sum is
**1410937920** - The reverse of 1108171519 is
**9151718011** - Previous prime number is
**29**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 34
- Digital Root 7

Name | one billion eight hundred forty-eight million nine hundred eighty-one thousand one hundred ninety-eight |
---|

- 1848981198 has 8 divisors, whose sum is
**3697962408** - The reverse of 1848981198 is
**8911898481** - Previous prime number is
**3**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 57
- Digital Root 3