Answer:
Range: {y ∈ ℝ : y ≤ -5}
Domain: {x ∈ ℝ : x ≥ 4}
Explanation:
The domain and range of f(x) are governed by the definition of the square root function. It only takes non-negative arguments, and it only produces non-negative results. This will mean ...
3x -12 ≥ 0 . . . the argument of the square root must not be negative
x ≥ 12/3 . . . . add 12 and divide by the coefficient of x
x ≥ 4 . . . . . . the domain of the function
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y = -√ -5 . . . . . . . abbreviated form of f(x) using √ to mean √(3x-12)
y +5 = -√ . . . . . . . add 5
-5 -y = √ . . . . . . . multiply by -1
-5 -y ≥ 0 . . . . . . . invoke the limitation on the output of √
-5 ≥ y . . . . . . . . . . add y . . . . . the range of the function