What are the domain and range of the real-valued function
f(x)=-3-sqrt 4x-12?
The domain of the function is all real numbers such that 4x - 12 ≥ 0, which means x ≥ 3. The domain is x ≥ 3.
To find the range of the function, we need to first determine the maximum value of the function. Since the square root function can only output non-negative values, the maximum value of -3 - sqrt(4x - 12) occurs when sqrt(4x - 12) = 0, which means the maximum value is -3.
Therefore, the range of the function is all real numbers such that f(x) ≤ -3. The range is f(x) ≤ -3.