Asked by j
Which statement is true about the function f(x)= –StartRoot negative x EndRoot?
The domain of the function is all negative real numbers.
The range of the function is all positive real numbers.
The domain and range of the function have opposite signs.
The domain and range of the function are the same.
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Correct answer: The domain and range of the function are the same.
Reason: f(x) = -√(-x) requires -x ≥ 0, so domain = {x ≤ 0}. For x ≤ 0, √(-x) ≥ 0, so f(x) ≤ 0, hence range = {y ≤ 0}. Thus domain and range are both all nonpositive real numbers.
Reason: f(x) = -√(-x) requires -x ≥ 0, so domain = {x ≤ 0}. For x ≤ 0, √(-x) ≥ 0, so f(x) ≤ 0, hence range = {y ≤ 0}. Thus domain and range are both all nonpositive real numbers.
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