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 | eight hundred seventeen million one hundred thirty-four thousand two hundred fifty-three |
---|

- 817134253 has 8 divisors, whose sum is
**890594208** - The reverse of 817134253 is
**352431718** - Previous prime number is
**83**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 34
- Digital Root 7

Name | six hundred thirty million six hundred twenty-seven thousand three hundred twenty-seven |
---|

- 630627327 has 16 divisors, whose sum is
**789058560** - The reverse of 630627327 is
**723726036** - Previous prime number is
**31**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 36
- Digital Root 9

Name | one hundred eighty-three million three hundred five thousand eight hundred twenty |
---|

- 183305820 has 32 divisors, whose sum is
**659901168** - The reverse of 183305820 is
**028503381** - Previous prime number is
**5**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 30
- Digital Root 3