Question

What are the domain and range of the real-valued function f(x) = -4 + √(3x-12)?

a. the domain is x<=4, and the range is f(x)>= -4.
b. the domain is x>=4, and the range is f(x)>= -4.
c. the domain is x>=4, and the range is f(x)<= -4.
d. the domain is x>=4, and the range is all real numbers.

Answer 1

The domain of the function f(x) = -4 + √(3x-12) is x >= 4, and the range is f(x) >= -4.

Step-by-step explanation:

The domain of the function f(x) = -4 + √(3x-12) is x ≥ 4. This is because the square root function is defined only for non-negative values, and the expression inside the square root must be greater than or equal to zero. So, 3x - 12 ≥ 0 which simplifies to x ≥ 4.

The range of the function is f(x) ≥ -4. This is because the square root function always produces non-negative values, and the constant term of -4 simply shifts the graph down by 4 units. So, the range of the function includes all values greater than or equal to -4.