Set the radicand in <math><mstyle displaystyle="true"><msqrt><mn>6</mn><mo>-</mo><mi>x</mi></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>6</mn></mstyle></math> from both sides of the inequality.

Multiply each term in <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi><mo>≥</mo><mo>-</mo><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math>

Multiply each term in <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi><mo>≥</mo><mo>-</mo><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

Multiply <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></mrow><mo>⋅</mo><mo>-</mo><mn>1</mn></mstyle></math> .

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

Multiply <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

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:

The range of an even indexed radical starts at its starting point <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>6</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> and extends to infinity.

Interval Notation:

Set-Builder Notation:

Determine the domain and range.

Domain: <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mi>∞</mi><mo>,</mo><mn>6</mn><mo>]</mo></mrow><mo>,</mo><mrow><mo>{</mo><mi>x</mi><mo>|</mo><mi>x</mi><mo>≤</mo><mn>6</mn><mo>}</mo></mrow></mstyle></math>

Range: <math><mstyle displaystyle="true"><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>{</mo><mi>y</mi><mo>|</mo><mi>y</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></mstyle></math>

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