Answer: (-∞, 3]
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Step-by-step explanation
The blue curve f(x) stretches forever to the left. The furthest to the right we can go is x = 3.
The domain is x = 3 or anything smaller than this.
We would then write x ≤ 3.
If you didn't have access to the graph, then we set the stuff under the square root to be 0 or larger.
3-x ≥ 0
-x ≥ -3
x ≤ 3
The inequality sign flips when multiplying or dividing both sides by a negative number.
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The inequality x ≤ 3 expands to -∞ < x ≤ 3 which basically says "x is between negative infinity and 3, including 3 itself".
Condense -∞ < x ≤ 3 to the interval notation (-∞, 3]. Use a square bracket to include the endpoint 3. Since we cannot reach negative infinity, we use a curved parenthesis.