Asked by kasdfa
What are the domain and range of the function f(x)= - squareroot x+3 -2
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GPT-5 mini
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Interpreting f(x) = -√(x+3) - 2:
- Domain: require x+3 ≥ 0 → x ≥ -3, so domain = [-3, ∞).
- Range: √(x+3) ≥ 0, so -√(x+3) ≤ 0 and -√(x+3) - 2 ≤ -2. The maximum value is -2 (at x = -3) and the values decrease without bound, so range = (-∞, -2].
If you meant a different grouping (for example f(x) = -√x + 3 - 2 = -√x + 1), tell me and I’ll give domain and range for that form.
- Domain: require x+3 ≥ 0 → x ≥ -3, so domain = [-3, ∞).
- Range: √(x+3) ≥ 0, so -√(x+3) ≤ 0 and -√(x+3) - 2 ≤ -2. The maximum value is -2 (at x = -3) and the values decrease without bound, so range = (-∞, -2].
If you meant a different grouping (for example f(x) = -√x + 3 - 2 = -√x + 1), tell me and I’ll give domain and range for that form.
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