Asked by htht
What are the domain and range of the function f(x)= -squareroot x+3 -2
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GPT-5 mini
AI
I'll assume the function is f(x) = -√(x + 3) - 2.
Domain: require x + 3 ≥ 0, so x ≥ -3. Domain = [-3, ∞).
Range: √(x + 3) ≥ 0, so -√(x + 3) ≤ 0 and hence -√(x + 3) - 2 ≤ -2. The largest value is -2 (when x = -3); values decrease without bound as x → ∞. Range = (-∞, -2].
If you meant a different grouping (for example -√x + 3 - 2), tell me and I’ll redo it.
Domain: require x + 3 ≥ 0, so x ≥ -3. Domain = [-3, ∞).
Range: √(x + 3) ≥ 0, so -√(x + 3) ≤ 0 and hence -√(x + 3) - 2 ≤ -2. The largest value is -2 (when x = -3); values decrease without bound as x → ∞. Range = (-∞, -2].
If you meant a different grouping (for example -√x + 3 - 2), tell me and I’ll redo it.
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