What are the domain and range of the function?
f(x)=^3√(x−3)
Domain: (−∞,∞)
Range: (−∞,∞)
Domain: [3,∞)
Range: [0,∞)
Domain: [0,∞)
Range: [3,∞)
Domain: [3,∞)
Range: (−∞,∞)
cube root has all reals for its domain.
To find the domain and range of the function f(x) = ∛(x - 3), let's start with the domain. The domain is basically the set of all possible x-values for which the function is defined.
In this function, we have a cube root (∛) of (x - 3). To ensure that the cube root is defined, the radicand (x - 3) must be greater than or equal to zero, since the cube root of a negative number is undefined in the real number system.
Setting (x - 3) ≥ 0, we get x ≥ 3. So the domain of the function is [3, ∞) which means that x can take any value greater than or equal to 3.
Now let's move on to finding the range. The range represents the set of all possible output or y-values of the function.
The cube root (∛) of any real number can produce both positive and negative values, so the range of the function is (-∞, ∞). This means that the function can output any real number, both positive and negative.
Therefore, the correct answer is:
Domain: [3, ∞)
Range: (-∞, ∞)