Set the radicand in <math><mstyle displaystyle="true"><msqrt><mi>x</mi><mo>-</mo><mn>3</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>3</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>3</mn></mstyle></math> in the expression.

Simplify the result.

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

The final answer is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

The radical expression end point is <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> .

Substitute the <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> value <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> into <math><mstyle displaystyle="true"><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><msqrt><mi>x</mi><mo>-</mo><mn>3</mn></msqrt></mstyle></math> . In this case, the point is <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>4</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>4</mn></mstyle></math> in the expression.

Simplify the result.

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</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> .

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>5</mn></mstyle></math> into <math><mstyle displaystyle="true"><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><msqrt><mi>x</mi><mo>-</mo><mn>3</mn></msqrt></mstyle></math> . In this case, the point is <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>5</mn><mo>,</mo><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>5</mn></mstyle></math> in the expression.

Simplify the result.

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><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><mn>3</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>1.41</mn><mo>)</mo></mrow></mstyle></math>

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Name | six hundred eighty-one million five hundred ninety-three thousand six hundred fifty-three |
---|

- 681593653 has 4 divisors, whose sum is
**734023948** - The reverse of 681593653 is
**356395186** - Previous prime number is
**13**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 46
- Digital Root 1

Name | one hundred three million nine hundred forty-one thousand three hundred forty-three |
---|

- 103941343 has 16 divisors, whose sum is
**119975040** - The reverse of 103941343 is
**343149301** - Previous prime number is
**211**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 28
- Digital Root 1

Name | one billion seven hundred sixty million six hundred forty-six thousand nine hundred fourteen |
---|

- 1760646914 has 8 divisors, whose sum is
**2844121980** - The reverse of 1760646914 is
**4196460671** - Previous prime number is
**13**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 44
- Digital Root 8