Final answer:
The domain of function p(x) = √x-1 +2 is the set of all x-values that are greater than or equal to 1, represented as [1, ∞). Therefore, option b. [1,[infinity]) is the correct choice.
Step-by-step explanation:
The domain of a function is the set of all possible input values (commonly called 'x-values') that will result in a valid output from a particular function.
When looking at the function p(x) = √x-1 +2, we need to consider when this function would be defined. Since you cannot take the square root of a negative number (in the real number system), the inside of the square root (the 'radicand') needs to be greater than or equal to zero. So, for the function to be valid, x-1 must be greater than or equal to 0.
By solving that inequality, we get x >= 1. This means that for all x-values greater than or equal to 1, we will get real-number outputs from the function. Therefore, the domain of this function p is [1, ∞), or option b from your choices.
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