State the domain and range of the function.
y=the cubed root of (x-2)
Thanks SO much!
To determine the domain and range of the function y = ∛(x-2), we can break it down step by step:
Step 1: Determine the Domain
The domain represents all the possible input values (x-values) for the function. In this case, we are taking the cubed root of the expression (x-2). However, keep in mind that the cubed root function (∛) is defined only for real numbers. Thus, the expression inside the cubed root (∛) should not be negative.
To find the allowable input values, we need to set the expression inside the cubed root (∛) to be greater than or equal to zero:
x - 2 ≥ 0
Solving for x:
x ≥ 2
Therefore, the domain of the function is all real numbers greater than or equal to 2: [2, ∞).
Step 2: Determine the Range
The range represents all the possible output values (y-values) for the function. Since the cubed root function (∛) is defined for all real numbers, there is no restriction on the output values.
Hence, the range of the function is all real numbers: (-∞, ∞).